Publications by Martin Leijnse

  • 2024
    • Supercurrent transport through - Abstract
      • We experimentally investigate supercurrent through Coulomb islands, where island and leads are fabricated from semiconducting nanowires with fully surrounding superconducting shells. Applying flux along the wire yields a series of destructive Little-Parks lobes with reentrant supercurrent. We find Coulomb blockade with 2$e$ peak spacing in the zeroth lobe and 1$e$ average spacing, with regions of significant even-odd modulation, in the first lobe. Evolution of Coulomb-peak amplitude through the first lobe is consistent with a theoretical model of supercurrent carried predominantly by zero-energy states in the leads and the island.
    • D. Razmadze, R. Seoane Souto, E. C. T. O'Farrell, P. Krogstrup, M. Leijnse, C. M. Marcus, S. Vaitiekėnas
      Journal reference: Phys. Rev. B 109, L041302 (2024) [pdf]
      DOI: 10.1103/PhysRevB.109.L041302

  • 2023
    • Tuning the Josephson diode response with an ac current - Abstract
      • Josephson diodes are superconducting elements that show an asymmetry in the critical current depending on the direction of the current. Here, we theoretically explore how an alternating current bias can tune the response of such a diode. We show that for slow driving there is always a regime where the system can only carry zero-voltage dc current in one direction, thus effectively behaving as an ideal Josephson diode. Under fast driving, the diode efficiency is also tunable, although the ideal regime cannot be reached in this case. We also investigate the residual dissipation due to the time-dependent current bias and show that it remains small. All our conclusions are solely based on the critical current asymmetry of the junction, and are thus compatible with any Josephson diode.
    • 2312.09204v1 [pdf]
      Rubén Seoane Souto, Martin Leijnse, Constantin Schrade, Marco Valentini, Georgios Katsaros, Jeroen Danon

    • Probing Majorana localization in minimal Kitaev chains through a quantum dot - Abstract
      • Artificial Kitaev chains, formed by quantum dots coupled via superconductors, have emerged as a promising platform for realizing Majorana bound states. Even a minimal Kitaev chain (a quantum dot--superconductor--quantum dot setup) can host Majorana states at discrete sweet spots. However, unambiguously identifying Majorana sweet spots in such a system is still challenging. In this work, we propose an additional dot coupled to one side of the chain as a tool to identify good sweet spots in minimal Kitaev chains. When the two Majorana states in the chain overlap, the extra dot couples to both and thus splits an even--odd ground-state degeneracy when its level is on resonance. In contrast, a ground-state degeneracy will persist for well-separated Majorana states. This difference can be used to identify points in parameter space with spatially separated Majorana states, using tunneling spectroscopy measurements. We perform a systematic analysis of different relevant situations. We show that the additional dot can help distinguishing between Majorana sweet spots and other trivial zero-energy crossings. We also characterize the different conductance patterns, which can serve as a guide for future experiments aiming to study Majorana states in minimal Kitaev chains.
    • Rubén Seoane Souto, Athanasios Tsintzis, Martin Leijnse, Jeroen Danon
      Journal reference: Phys. Rev. Research 5, 043182 (2023) [pdf]
      DOI: 10.1103/PhysRevResearch.5.043182

    • Nonsinusoidal current-phase relations in semiconductor–superconductor– ferromagnetic insulator devices - Abstract
      • Coherent tunneling processes of multiple Cooper pairs across a Josephson junction give rise to higher harmonics in the current phase relation. In this work, we propose and study Josephson junctions based on semiconductor-superconductor-ferromagnetic insulator heterostructures to engineer nonsinusoidal current-phase relations. The gate-tunability of charge carriers density in the semiconductor, together with the adjustable magnetization of the ferromagnetic insulator, provides control over the content of the supercurrent harmonics. At finite exchange field, hybrid junctions can undergo a 0\,--\,$\pi$ phase transition, resulting in the supercurrent reversal. Close to the transition, single-pair tunneling is suppressed and the current-phase relation is dominated by the second-harmonic, indicating transport primarily by pairs of Cooper pairs. Finally, we demonstrate that non-collinear magnetization or spin-orbit coupling in the leads and the junction can lead to a gate-tunable Josephson diode effect with efficiencies of up to $\sim30\%$.
    • Andrea Maiani, Karsten Flensberg, Martin Leijnse, Constantin Schrade, Saulius Vaitiekėnas, Rubén Seoane Souto
      Journal reference: Phys. Rev. B 107, 245415 (2023) [pdf]
      DOI: 10.1103/PhysRevB.107.245415

    • A fermion-parity qubit in a proximitized double quantum dot - Abstract
      • Bound states in quantum dots coupled to superconductors can be in a coherent superposition of states with different electron number but with the same number parity. Electrostatic gating can tune this superposition to a sweet spot, where the quantum dot has the same mean electric charge independent of its electron-number parity. Here, we propose to encode quantum information in the local fermion parity of two tunnel-coupled quantum dots embedded in a Josephson junction. At the sweet spot, the qubit states have zero charge dipole moment. This protects the qubit from dephasing due to electric field fluctuations. Depending on the strength of the tunnel coupling between the dots, the system is further protected towards either relaxation (weak tunneling) or dephasing (strong tunneling) from noise coupling separately to each quantum dot. We describe initialization and readout as well as single-qubit and two-qubit gates by pulsing gate voltages.
    • 2307.05678v1 [pdf]
      Max Geier, Rubén Seoane Souto, Jens Schulenborg, Serwan Asaad, Martin Leijnse, Karsten Flensberg

    • Detecting Majorana modes by readout of poisoning-induced parity flips - Abstract
      • Reading out the parity degree of freedom of Majorana bound states is key to demonstrating their nonabelian exchange properties. Here, we present a low-energy model describing localized edge states in a two-arm device. We study parity-to-charge conversion based on coupling the superconductor bound states to a quantum dot whose charge is read out by a sensor. The dynamics of the system, including the readout device, is analyzed in full using a quantum-jump approach. We show how the resulting signal and noise ratio differentiates between local Majorana and Andreev bound states.
    • Jens Schulenborg, Svend Krøjer, Michele Burrello, Martin Leijnse, Karsten Flensberg
      Journal reference: Phys. Rev. B 107, L121401 (2023) [pdf]
      DOI: 10.1103/PhysRevB.107.L121401

  • 2022
    • Multiterminal transport spectroscopy of subgap states in Coulomb-blockaded superconductors - Abstract
      • Subgap states are responsible for the low-bias transport features of hybrid superconducting--semiconducting devices. Here, we analyze the local and nonlocal differential conductance of Coulomb-blockaded multiterminal superconducting islands that host subgap states with different spatial structures. The emerging patterns of their transport spectroscopy are used to characterize the possible topological nature of these devices and offer the possibility of controlling their transport properties. We develop a next-to-leading order master equation to describe the multiterminal transport in superconductors with both strong Coulomb interactions and multiple subgap states, coupled with metallic leads. We show that the nonlocal differential conductance characterizes the spatial extension of the subgap states and signals the presence of degenerate bound states with a finite support on different parts of the device. Additionally, it displays sharp sign changes as a function of the induced charge of the superconductor, signaling energy crossings among its lowest excited states.
    • Rubén Seoane Souto, Matteo M. Wauters, Karsten Flensberg, Martin Leijnse, Michele Burrello
      Journal reference: Phys. Rev. B 106, 235425 (2022) [pdf]
      DOI: 10.1103/PhysRevB.106.235425

    • Semiconductor-ferromagnet-superconductor planar heterostructures for 1D topological superconductivity - Abstract
      • Hybrid structures of semiconducting (SM) nanowires, epitaxially grown superconductors (SC), and ferromagnetic-insulator (FI) layers have been explored experimentally and theoretically as alternative platforms for topological superconductivity at zero magnetic field. Here, we analyze a tripartite SM/FI/SC heterostructure but realized in a planar stacking geometry, where the thin FI layer acts as a spin-polarized tunneling barrier between the SM and the SC. We optimize the system's geometrical parameters using microscopic simulations, finding the range of FI thicknesses for which the hybrid system can be tuned into the topological regime. Within this range, and thanks to the vertical confinement provided by the stacking geometry, trivial and topological phases alternate regularly as the external gate is varied, displaying a hard topological gap that can reach half of the SC one. This is a significant improvement compared to setups using hexagonal nanowires, which show erratic topological regions with typically smaller and softer gaps. Our proposal provides a magnetic field-free planar design for quasi-one-dimensional topological superconductivity with attractive properties for experimental control and scalability.
    • Samuel D. Escribano, Andrea Maiani, Martin Leijnse, Karsten Flensberg, Yuval Oreg, Alfredo Levy Yeyati, Elsa Prada, Rubén Seoane Souto
      Journal reference: npj Quantum Materials 7, 81 (2022) [pdf]
      DOI: 10.1038/s41535-022-00489-9

    • Josephson Diode Effect in Supercurrent Interferometers - Abstract
      • A Josephson diode is a non-reciprocal circuit element that supports a larger dissipationless supercurrent in one direction than in the other. In this work, we propose and theoretically study a class of Josephson diodes based on supercurrent interferometers containing mesoscopic Josephson junctions, such as point contacts or quantum dots, which are not diodes themselves but possess non-sinusoidal current-phase relations. We show that such Josephson diodes have several important advantages, like being electrically tunable and requiring neither Zeeman splitting nor spin-orbit coupling, only time-reversal breaking by a magnetic flux. We also show that our diodes have a characteristic AC response, revealed by the Shapiro steps. Even the simplest realization of our Josephson diode paradigm that relies on only two junctions can achieve efficiencies of up to $\sim40\%$ and, interestingly, far greater efficiencies are achievable by concatenating multiple interferometer loops.
    • Rubén Seoane Souto, Martin Leijnse, Constantin Schrade
      Journal reference: Phys. Rev. Lett. 129, 267702 (2022) [pdf]
      DOI: 10.1103/PhysRevLett.129.267702

    • Fusion rules in a Majorana single-charge transistor - Abstract
      • A demonstration of the theoretically predicted non-abelian properties of Majorana bound states (MBSs) would constitute a definite proof of a topological superconducting phase. Alongside the nontrivial braiding statistics, the fusion rules are fundamental properties of all non-abelian anyons. In this work, we propose and theoretically analyze a way to demonstrate MBS fusion rules in a Majorana single-charge transistor. Our proposal reduces both the number of operations and the device complexity compared to previous designs. Furthermore, we show that the fusion protocol can be adapted to pump a quantized amount of charge in each cycle, providing a straightforward method to detect fusion rules through a DC current measurement. We analyze the protocol numerically and analytically and show that the required operational timescales and expected measurement signals are within experimental capabilities in various superconductor-semiconductor hybrid platforms.
    • R. Seoane Souto, M. Leijnse
      Journal reference: SciPost Phys. 12, 161 (2022) [pdf]
      DOI: 10.21468/SciPostPhys.12.5.161

    • Evidence for spin-polarized bound states in semiconductor–superconductor–ferromagnetic-insulator islands - Abstract
      • We report Coulomb blockade transport studies of semiconducting InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. Comparing experiment to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels. Results are consistent with zero-field spin splitting exceeding the induced superconducting gap. Energies of subgap states are tunable on either side of zero via electrostatic gates.
    • S. Vaitiekėnas, R. Seoane Souto, Y. Liu, P. Krogstrup, K. Flensberg, M. Leijnse, C. M. Marcus
      Journal reference: Phys. Rev. B 105, L041304 (2022) [pdf]
      DOI: 10.1103/PhysRevB.105.L041304

  • 2021
    • Dynamic impurities in two-dimensional topological insulator edge states - Abstract
      • Helical edge states of two-dimensional topological insulators show a gap in the Density of States (DOS) and suppressed conductance in the presence of ordered magnetic impurities. Here we will consider the dynamical effects on the DOS and transmission when the magnetic impurities are driven periodically. Using the Floquet formalism and Green's functions, the system properties are studied as a function of the driving frequency and the potential energy contribution of the impurities. We see that increasing the potential part closes the DOS gap for all driving regimes. The transmission gap is also closed, showing an pronounced asymmetry as a function of energy. These features indicate that the dynamical transport properties could yield valuable information about the magnetic impurities.
    • 2107.00994v1 [pdf]
      Simon Wozny, Martin Leijnse, Sigurdur I. Erlingsson

    • Quantum confinement suppressing electronic heat flow below the Wiedemann-Franz law - Abstract
      • The Wiedemann-Franz law states that the charge conductance and the electronic contribution to the heat conductance are proportional. This sets stringent constraints on efficiency bounds for thermoelectric applications, which seek for large charge conduction in response to a small heat flow. We present experiments based on a quantum dot formed inside a semiconducting InAs nanowire transistor, in which the heat conduction can be tuned significantly below the Wiedemann-Franz prediction. Comparison with scattering theory shows that this is caused by quantum confinement and the resulting energy-selective transport properties of the quantum dot. Our results open up perspectives for tailoring independently the heat and electrical conduction properties in semiconductor nanostructures.
    • 2106.06229v1 [pdf]
      D. Majidi, M. Josefsson, M. Kumar, M. Leijnse, L. Samuelson, H. Courtois, C. B. Winkelmann, V. F. Maisi

    • Multilevel effects in quantum dot based parity-to-charge conversion of Majorana box qubits - Abstract
      • Quantum-dot based parity-to-charge conversion is a promising method for reading out quantum information encoded nonlocally into pairs of Majorana zero modes. To obtain a sizable parity-to-charge visibility, it is crucial to tune the relative phase of the tunnel couplings between the dot and the Majorana modes appropriately. However, in the presence of multiple quasi-degenerate dot orbitals, it is in general not experimentally feasible to tune all couplings individually. This paper shows that such configurations could make it difficult to avoid a destructive multi-orbital interference effect that substantially reduces the read-out visibility. We analyze this effect using a Lindblad quantum master equation. This exposes how the experimentally relevant system parameters enhance or suppress the visibility when strong charging energy, measurement dissipation and, most importantly, multi-orbital interference is accounted for. In particular, we find that an intermediate-time readout could mitigate some of the interference-related visibility reductions affecting the stationary limit.
    • Jens Schulenborg, Michele Burrello, Martin Leijnse, Karsten Flensberg
      Journal reference: Phys. Rev. B 103, 245407 (2021) [pdf]
      DOI: 10.1103/PhysRevB.103.245407

    • Symmetry-controlled singlet-triplet transition in a double-barrier quantum ring - Abstract
      • We engineer a system of two strongly confined quantum dots to gain reproducible electrostatic control of the spin at zero magnetic field. Coupling the dots in a tight ring-shaped potential with two tunnel barriers, we demonstrate that an electric field can switch the electron ground state between a singlet and a triplet configuration. Comparing our experimental co-tunneling spectroscopy data to a full many-body treatment of interacting electrons in a double-barrier quantum ring, we find excellent agreement in the evolution of many-body states with electric and magnetic fields. The calculations show that the singlet-triplet energy crossover, not found in conventionally coupled quantum dots, is made possible by the ring-shaped geometry of the confining potential.
    • 2104.11561v1 [pdf]
      Heidi Potts, Josef Josefi, I-Ju Chen, Sebastian Lehmann, Kimberly A. Dick, Martin Leijnse, Stephanie M. Reimann, Jakob Bengtsson, Claes Thelander

    • Spin-polarized bound states in semiconductor-superconductor-ferromagnetic insulator islands - Abstract
      • We report Coulomb blockade transport studies of InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. By comparing experimental results to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels, indicating that spin splitting exceeding the induced superconducting gap at zero applied magnetic field. Energies of the polarized subgap states can be tuned on either side of zero by electrostatic gates.
    • 2104.01463v1 [pdf]
      S. Vaitiekėnas, R. Seoane Souto, Y. Liu, P. Krogstrup, K. Flensberg, M. Leijnse, C. M. Marcus

    • Topological superconductivity in semiconductor–superconductor–magnetic-insulator heterostructures - Abstract
      • Hybrid superconductor-semiconductor heterostructures are promising platforms for realizing topological superconductors and exploring Majorana bound states physics. Motivated by recent experimental progress, we theoretically study how magnetic insulators offer an alternative to the use of external magnetic fields for reaching the topological regime. We consider different setups, where: (1) the magnetic insulator induces an exchange field in the superconductor, which leads to a splitting in the semiconductor by proximity effect, and (2) the magnetic insulator acts as a spin-filter tunnel barrier between the superconductor and the semiconductor. We show that the spin splitting in the superconductor alone cannot induce a topological transition in the semiconductor. To overcome this limitation, we propose to use a spin-filter barrier that enhances the magnetic exchange and provides a mechanism for a topological phase transition. Moreover, the spin-dependent tunneling introduces a strong dependence on the band alignment, which can be crucial in quantum-confined systems. This mechanism opens up a route towards networks of topological wires with fewer constraints on device geometry compared to previous devices that require external magnetic fields.
    • A. Maiani, R. Seoane Souto, M. Leijnse, K. Flensberg
      Journal reference: Phys. Rev. B 103, 104508 (2021) [pdf]
      DOI: 10.1103/PhysRevB.103.104508

  • 2020
    • Band structure and end states in InAs/GaSb core-shell-shell nanowires - Abstract
      • Quantum wells in InAs/GaSb heterostructures can be tuned to a topological regime associated with the quantum spin Hall effect, which arises due to an inverted band gap and hybridized electron and hole states. Here, we investigate electron-hole hybridization and the fate of the quantum spin Hall effect in a quasi one-dimensional geometry, realized in a core-shell-shell nanowire with an insulator core and InAs and GaSb shells. We calculate the band structure for an infinitely long nanowire using $\mathbf{k \cdot p}$ theory within the Kane model and the envelope function approximation, then map the result onto a BHZ model which is used to investigate finite-length wires. Clearly, quantum spin Hall edge states cannot appear in the core-shell-shell nanowires which lack one-dimensional edges, but in the inverted band-gap regime we find that the finite-length wires instead host localized states at the wire ends. These end states are not topologically protected, they are four-fold degenerate and split into two Kramers pairs in the presence of potential disorder along the axial direction. However, there is some remnant of the topological protection of the quantum spin Hall edge states in the sense that the end states are fully robust to (time-reversal preserving) angular disorder, as long as the bulk band gap is not closed.
    • Florinda Viñas Boström, Athanasios Tsintzis, Michael Hell, Martin Leijnse
      DOI: 10.1103/PhysRevB.102.195434
      2007.05391v1 [pdf]

    • Selective tuning of spin-orbital Kondo contributions in parallel-coupled quantum dots - Abstract
      • We use co-tunneling spectroscopy to investigate spin-, orbital-, and spin-orbital Kondo transport in a strongly confined system of InAs double quantum dots (QDs) parallel-coupled to source and drain. In the one-electron transport regime, the higher symmetry spin-orbital Kondo effect manifests at orbital degeneracy and no external magnetic field. We then proceed to show that the individual Kondo contributions can be isolated and studied separately; either by orbital detuning in the case of spin-Kondo transport, or by spin splitting in the case of orbital Kondo transport. By varying the inter-dot tunnel coupling, we show that lifting of the spin degeneracy is key to confirming the presence of an orbital degeneracy, and to detecting a small orbital hybridization gap. Finally, in the two-electron regime, we show that the presence of a spin-triplet ground state results in spin-Kondo transport at zero magnetic field.
    • Heidi Potts, Martin Leijnse, Adam Burke, Malin Nilsson, Sebastian Lehmann, Kimberly A. Dick, Claes Thelander
      Journal reference: Phys. Rev. B 101, 115429 (2020) [pdf]
      DOI: 10.1103/PhysRevB.101.115429

    • Double quantum-dot engine fueled by entanglement between electron spins - Abstract
      • The laws of thermodynamics allow work extraction from a single heat bath provided that the entropy decrease of the bath is compensated for by another part of the system. We propose a thermodynamic quantum engine that exploits this principle and consists of two electrons on a double quantum dot (QD). The engine is fueled by providing it with singlet spin states, where the electron spins on different QDs are maximally entangled, and its operation involves only changing the tunnel coupling between the QDs. Work can be extracted since the entropy of an entangled singlet is lower than that of a thermal (mixed) state, although they look identical when measuring on a single QD. We show that the engine is an optimal thermodynamic engine in the long-time limit. In addition, we include a microscopic description of the bath and analyze the engine's finite-time performance using experimentally relevant parameters.
    • Martin Josefsson, Martin Leijnse
      Journal reference: Phys. Rev. B 101, 081408 (2020) [pdf]
      DOI: 10.1103/PhysRevB.101.081408

    • Timescales for charge transfer based operations on Majorana systems - Abstract
      • In this article we analyze the efficiency of operations based on transferring charge from a quantum dot (QD) to two coupled topological superconductors, which can be used for performing nonabelian operations on Majorana bound states (MBSs). We develop a method which allows us to describe the full time-evolution of the system as the QD energy is manipulated. Using a full counting statistics analysis, we set bounds to the operation time scales. The lower bound depends on the superconducting phase difference due to a partial decoupling of the different MBSs parity sectors, while the upper bound is set by the tunneling of quasiparticles to the MBSs. Using realistic parameters, we find the existence of a regime where the operation can be carried out with a fidelity close to unity. Finally, we propose the use of a two operations protocol to quantify the effect of the dephasing and accumulated dynamical phases, demonstrating their absence for certain superconducting phase differences.
    • R. Seoane Souto, K. Flensberg, M. Leijnse
      Journal reference: Phys. Rev. B 101, 081407 (2020) [pdf]
      DOI: 10.1103/PhysRevB.101.081407

  • 2019
    • Optimal power and efficiency of single quantum dot heat engines: Theory and experiment - Abstract
      • Quantum dots (QDs) can serve as near perfect energy filters and are therefore of significant interest for the study of thermoelectric energy conversion close to thermodynamic efficiency limits. Indeed, recent experiments in [Nat. Nano. 13, 920 (2018)] realized a QD heat engine with performance near these limits and in excellent agreement with theoretical predictions. However, these experiments also highlighted a need for more theory to help guide and understand the practical optimization of QD heat engines, in particular regarding the role of tunnel couplings on the performance at maximum power and efficiency for QDs that couple seemingly weakly to electronic reservoirs. Furthermore, these experiments also highlighted the critical role of the external load when optimizing the performance of a QD heat engine in practice. To provide further insight into the operation of these engines we use the Anderson impurity model together with a Master equation approach to perform power and efficiency calculations up to co-tunneling order. This is combined with additional thermoelectric experiments on a QD embedded in a nanowire where the power is measured using two methods. We use the measurements to present an experimental procedure for efficiently finding the external load $R_P$ which should be connected to the engine to optimize power output. Our theoretical estimates of $R_P$ show a good agreement with the experimental results, and we show that second order tunneling processes and non-linear effects have little impact close to maximum power, allowing us to derive a simple analytic expression for $R_P$. In contrast, we find that the electron contribution to the thermoelectric efficiency is significantly reduced by second order tunneling processes, even for rather weak tunnel couplings.
    • Martin Josefsson, Artis Svilans, Heiner Linke, Martin Leijnse
      Journal reference: Phys. Rev. B 99, 235432 (2019) [pdf]
      DOI: 10.1103/PhysRevB.99.235432

    • Electrical control of spins and giant g-factors in ring-like coupled quantum dots - Abstract
      • Emerging theoretical concepts for quantum technologies have driven a continuous search for structures where a quantum state, such as spin, can be manipulated efficiently. Central to many concepts is the ability to control a system by electric and magnetic fields, relying on strong spin-orbit interaction and a large g-factor. Here, we present a new mechanism for spin and orbital manipulation using small electric and magnetic fields. By hybridizing specific quantum dot states at two points inside InAs nanowires, nearly perfect quantum rings form. Large and highly anisotropic effective g-factors are observed, explained by a strong orbital contribution. Importantly, we find that the orbital and spin-orbital contributions can be efficiently quenched by simply detuning the individual quantum dot levels with an electric field. In this way, we demonstrate not only control of the effective g-factor from 80 to almost 0 for the same charge state, but also electrostatic change of the ground state spin.
    • Heidi Potts, I-Ju Chen, Athanasios Tsintzis, Malin Nilsson, Sebastian Lehmann, Kimberly A. Dick, Martin Leijnse, Claes Thelander
      Journal reference: Nature Communications 10, 5740 (2019) [pdf]
      DOI: 10.1038/s41467-019-13583-7

    • Quantum interference in transport through almost symmetric double quantum dots - Abstract
      • We theoretically investigate transport signatures of quantum interference in highly symmetric double quantum dots in a parallel geometry and demonstrate that extremely weak symmetry-breaking effects can have a dramatic influence on the current. Our calculations are based on a master equation where quantum interference enters as non-diagonal elements of the density matrix of the double quantum dots. We also show that many results have a physically intuitive meaning when recasting our equations as Bloch-like equations for a pseudo spin associated with the dot occupation. In the perfectly symmetric configuration with equal tunnel couplings and orbital energies of both dots, there is no unique stationary state density matrix. Interestingly, however, adding arbitrarily small symmetry-breaking terms to the tunnel couplings or orbital energies stabilizes a stationary state either with or without quantum interference, depending on the competition between these two perturbations. The different solutions can correspond to very different current levels. Therefore, if the orbital energies and/or tunnel couplings are controlled by, e.g., electrostatic gating, the double quantum dot can act as an exceptionally sensitive electric switch.
    • Zeng-Zhao Li, Martin Leijnse
      Journal reference: Phys. Rev. B 99, 125406 (2019) [pdf]
      DOI: 10.1103/PhysRevB.99.125406

  • 2018
    • Tuning the Two-Electron Hybridization and Spin States in Parallel-Coupled InAs Quantum Dots - Abstract
      • We study spin transport in the one- and two-electron regimes of parallel-coupled double quantum dots (DQDs). The DQDs are formed in InAs nanowires by a combination of crystal-phase engineering and electrostatic gating, with an interdot tunnel coupling ($t$) tunable by one order of magnitude. Large single-particle energy separations (up to 10 meV) and $|g^*|$ factors ($\sim$10) enable detailed studies of the $B$-field-induced transition from a singlet-to-triplet ground state as a function of $t$. In particular, we investigate how the magnitude of the spin-orbit-induced singlet-triplet anticrossing depends on $t$. For cases of strong coupling, we find values of 230 $\mu$eV for the anticrossing using excited-state spectroscopy. Experimental results are reproduced by calculations based on rate equations and a DQD model including a single orbital in each dot.
    • Malin Nilsson, Florinda Viñas Boström, Sebastian Lehmann, Kimberly A. Dick, Martin Leijnse, Claes Thelander
      Journal reference: Phys. Rev. Lett. 121, 156802 (2018) [pdf]
      DOI: 10.1103/PhysRevLett.121.156802

    • Spectroscopy and level detuning of few-electron spin states in parallel InAs quantum dots - Abstract
      • We use tunneling spectroscopy to study the evolution of few-electron spin states in parallel InAs nanowire double quantum dots (QDs) as a function of level detuning and applied magnetic field. Compared to the much more studied serial configuration, parallel coupling of the QDs to source and drain greatly expands the probing range of excited state transport. Owing to a strong confinement, we can here isolate transport involving only the very first interacting single QD orbital pair. For the (2,0)-(1,1) charge transition, with relevance for spin-based qubits, we investigate the excited (1,1) triplet, and hybridization of the (2,0) and (1,1) singlets. An applied magnetic field splits the (1,1) triplet, and due to spin-orbit induced mixing with the (2,0) singlet, we clearly resolve transport through all triplet states near the avoided singlet-triplet crossings. Transport calculations, based on a simple model with one orbital on each QD, fully replicate the experimental data. Finally, we observe an expected mirrored symmetry between the 1-2 and 2-3 electron transitions resulting from the two-fold spin degeneracy of the orbitals.
    • Claes Thelander, Malin Nilsson, Florinda Viñas Boström, Adam Burke, Sebastian Lehmann, Kimberly A. Dick, Martin Leijnse
      Journal reference: Phys. Rev. B 98, 245305 (2018) [pdf]
      DOI: 10.1103/PhysRevB.98.245305

    • Thermoelectric Characterization of the Kondo Resonance in Nanowire Quantum Dots - Abstract
      • We experimentally verify hitherto untested theoretical predictions about the thermoelectric properties of Kondo correlated quantum dots (QDs). The specific conditions required for this study are obtained by using QDs epitaxially grown in nanowires, combined with a recently developed method for controlling and measuring temperature differences at the nanoscale. This makes it possible to obtain data of very high quality both below and above the Kondo temperature, and allows a quantitative comparison with theoretical predictions. Specifically, we verify that Kondo correlations can induce a polarity change of the thermoelectric current, which can be reversed either by increasing the temperature or by applying a magnetic field.
    • Artis Svilans, Martin Josefsson, Adam M. Burke, Sofia Fahlvik, Claes Thelander, Heiner Linke, Martin Leijnse
      Journal reference: Phys. Rev. Lett. 121, 206801 (2018) [pdf]
      DOI: 10.1103/PhysRevLett.121.206801

    • A quantum-dot heat engine operating close to the thermodynamic efficiency limits - Abstract
      • Cyclical heat engines are a paradigm of classical thermodynamics, but are impractical for miniaturization because they rely on moving parts. A more recent concept is particle-exchange (PE) heat engines, which uses energy filtering to control a thermally driven particle flow between two heat reservoirs. As they do not require moving parts and can be realized in solid-state materials, they are suitable for low-power applications and miniaturization. It was predicted that PE engines could reach the same thermodynamically ideal efficiency limits as those accessible to cyclical engines, but this prediction has not been verified experimentally. Here, we demonstrate a PE heat engine based on a quantum dot (QD) embedded into a semiconductor nanowire. We directly measure the engine's steady-state electric power output and combine it with the calculated electronic heat flow to determine the electronic efficiency $\eta$. We find that at the maximum power conditions, $\eta$ is in agreement with the Curzon-Ahlborn efficiency and that the overall maximum $\eta$ is in excess of 70$\%$ of the Carnot efficiency while maintaining a finite power output. Our results demonstrate that thermoelectric power conversion can, in principle, be achieved close to the thermodynamic limits, with direct relevance for future hot-carrier photovoltaics, on-chip coolers or energy harvesters for quantum technologies.
    • Martin Josefsson, Artis Svilans, Adam M. Burke, Eric A. Hoffmann, Sofia Fahlvik, Claes Thelander, Martin Leijnse, Heiner Linke
      Journal reference: Nature Nanotechnology 13, 920-924 (2018) [pdf]
      DOI: 10.1038/s41565-018-0200-5

    • Four-Majorana qubit with charge readout: Dynamics and decoherence - Abstract
      • We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the charge-stability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multi-level spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a non-Markovian environment. In particular, we study a gate-controlled protocol where conversion between Coulomb-blockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection.
    • Tommy Li, William A. Coish, Michael Hell, Karsten Flensberg, Martin Leijnse
      Journal reference: Phys. Rev. B 98, 205403 (2018) [pdf]
      DOI: 10.1103/PhysRevB.98.205403

    • Distinguishing Majorana bound states from localized Andreev bound states by interferometry - Abstract
      • Experimental evidence for Majorana bound states (MBSs) is so far mainly based on the robustness of a zero-bias conductance peak. However, similar features can also arise due to Andreev bound states (ABSs) localized at the end of an island. We show that these two scenarios can be distinguished by an interferometry experiment based on embedding a Coulomb-blockaded island into an Aharonov-Bohm ring. For two ABSs, when the ground state is nearly degenerate, cotunneling can change the state of the island and interference is suppressed. By contrast, for two MBSs the ground state is nondegenerate and cotunneling has to preserve the island state, which leads to $h / e$-periodic conductance oscillations with magnetic flux. Such interference setups can be realized with semiconducting nanowires or two-dimensional electron gases with proximity-induced superconductivity and may also be a useful spectroscopic tool for parity-flip mechanisms.
    • Michael Hell, Karsten Flensberg, Martin Leijnse
      Journal reference: Phys. Rev. B 97, 161401 (2018) [pdf]
      DOI: 10.1103/PhysRevB.97.161401

    • Anharmonicity of a superconducting qubit with a few-mode Josephson junction - Abstract
      • Coherent operation of gate-voltage-controlled hybrid transmon qubits (gatemons) based on semiconductor nanowires was recently demonstrated. Here we experimentally investigate the anharmonicity in epitaxial InAs-Al Josephson junctions, a key parameter for their use as a qubit. Anharmonicity is found to be reduced by roughly a factor of two compared to conventional metallic junctions, and dependent on gate voltage. Experimental results are consistent with a theoretical model, indicating that Josephson coupling is mediated by a small number of highly transmitting modes in the semiconductor junction.
    • A. Kringhøj, L. Casparis, M. Hell, T. W. Larsen, F. Kuemmeth, M. Leijnse, K. Flensberg, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus
      Journal reference: Phys. Rev. B 97, 060508 (2018) [pdf]
      DOI: 10.1103/PhysRevB.97.060508

  • 2017
    • QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices - Abstract
      • QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron-electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), first-order Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches.
    • Gediminas Kiršanskas, Jonas Nyvold Pedersen, Olov Karlström, Martin Leijnse, Andreas Wacker
      Journal reference: Comput. Phys. Commun. 221, 317 (2017) [pdf]
      DOI: 10.1016/j.cpc.2017.07.024

    • Coupling and braiding Majorana bound states in networks defined in two-dimensional electron gases with proximity-induced superconductivity - Abstract
      • Two-dimensional electron gases with strong spin-orbit coupling covered by a superconducting layer offer a flexible and potentially scalable platform for Majorana networks. We predict Majorana bound states (MBSs) to appear for experimentally achievable parameters and realistic gate potentials in two designs: either underneath a narrow stripe of a superconducting layer (S-stripes) or where a narrow stripe has been removed from a uniform layer (N-stripes). The coupling of the MBSs can be tuned for both types in a wide range (< 1 neV to >10 $\mu$eV) using gates placed adjacent to the stripes. For both types, we numerically compute the local density of states for two parallel Majorana-stripe ends as well as Majorana trijunctions formed in a tuning-fork geometry. The MBS coupling between parallel Majorana stripes can be suppressed below 1 neV for potential barriers in the meV range for separations of about 200 nm. We further show that the MBS couplings in a trijunction can be gate-controlled in a range similar to the intra-stripe coupling while maintaining a sizable gap to the excited states (tens of $\mu$eV). Altogether, this suggests that braiding can carried out on a time scale of 10-100 ns.
    • Michael Hell, Karsten Flensberg, Martin Leijnse
      Journal reference: Phys. Rev. B 96, 035444 (2017) [pdf]
      DOI: 10.1103/PhysRevB.96.035444

    • Extracting band structure characteristics of GaSb/InAs core-shell nanowires from thermoelectric properties - Abstract
      • Nanowires with a GaSb core and an InAs shell (and the inverted structure) are interesting for studies of electron-hole hybridization and interaction effects due to the bulk broken band-gap alignment at the material interface. We have used eight-band $\mathbf{k\cdot p}$ theory together with the envelope function approximation to calculate the band structure of such nanowires. For a fixed core radius, as a function of shell thickness the band structure changes from metallic (for a thick shell) to semiconducting (for a thin shell) with a gap induced by quantum confinement. For intermediate shell thickness, a different gapped band structure can appear, where the gap is induced by hybridization between the valence band in GaSb and the conduction band in InAs. To establish a relationship between the nanowire band structures and signatures in thermoelectrical measurements, we use the calculated energy dispersions as input to the Boltzmann equation and to ballistic transport equations to study the diffusive limit and the ballistic limit, respectively. Our theoretical results provide a guide for experiments, showing how thermoelectric measurements in a gated setup can be used to distinguish between different types of band gaps, or tune the system into a regime with few electrons and few holes, which can be of interest for studies of exciton physics.
    • Florinda Viñas, H. Q. Xu, Martin Leijnse
      Journal reference: Phys. Rev. B 95, 115420 (2017) [pdf]
      DOI: 10.1103/PhysRevB.95.115420

    • Two-Dimensional Platform for Networks of Majorana Bound States - Abstract
      • We model theoretically a two-dimensional electron gas (2DEG) covered by a superconductor and demonstrate that topological superconducting channels are formed when stripes of the superconducting layer are removed. As a consequence, Majorana bound states (MBS) are created at the ends of the stripes. We calculate the topological invariant and energy gap of a single stripe, using realistic values for an InAs 2DEG proximitized by an epitaxial Al layer. We show that the topological gap is enhanced when the structure is made asymmetric. This can be achieved by either imposing a phase difference (by driving a supercurrent or using a magnetic-flux loop) over the strip or by replacing one superconductor by a metallic gate. Both strategies also enable control over the MBS splitting, thereby facilitating braiding and readout schemes based on controlled fusion of MBS. Finally, we outline how a network of Majorana stripes can be designed.
    • Michael Hell, Martin Leijnse, Karsten Flensberg
      Journal reference: Phys. Rev. Lett. 118, 107701 (2017) [pdf]
      DOI: 10.1103/PhysRevLett.118.107701

  • 2016
    • Majorana bound state in a coupled quantum-dot hybrid-nanowire system - Abstract
      • Hybrid nanowires combining semiconductor and superconductor materials appear well suited for the creation, detection, and control of Majorana bound states (MBSs). We demonstrate the emergence of MBSs from coalescing Andreev bound states (ABSs) in a hybrid InAs nanowire with epitaxial Al, using a quantum dot at the end of the nanowire as a spectrometer. Electrostatic gating tuned the nanowire density to a regime of one or a few ABSs. In an applied axial magnetic field, a topological phase emerges in which ABSs move to zero energy and remain there, forming MBSs. We observed hybridization of the MBS with the end-dot bound state, which is in agreement with a numerical model. The ABS/MBS spectra provide parameters that are useful for understanding topological superconductivity in this system.
    • M. T. Deng, S. Vaitiekenas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup, C. M. Marcus
      Journal reference: Science 354, 1557-1562 (2016) [pdf]
      DOI: 10.1126/science.aaf3961

    • Experiments on the thermoelectric properties of quantum dots - Abstract
      • Quantum dots (QDs) are good model systems for fundamental studies of mesoscopic transport phenomena using thermoelectric effects because of their small size, electrostatically tunable properties and thermoelectric response characteristics that are very sensitive to small thermal biases. Here we provide a review of experimental studies on thermoelectric properties of single QDs realized in two-dimensional electron gases, single-walled carbon nanotubes and semiconductor nanowires. A key requirement for such experiments is methods for nanoscale thermal biasing. We briefly review the main techniques used in the field, namely, heating of the QD contacts, side heating and top heating, and touch upon their relative advantages. The thermoelectric response of a QD as a function of gate potential has a characteristic oscillatory behavior with the same period as is observed for conductance peaks. Much of the existing literature focuses on the agreement between experiments and theory, particularly for amplitude and line-shape of the thermovoltage $V_{th}$. A general observation is that the widely used single-electron tunneling approximation for QDs has limited success in reproducing measured $V_{th}$. Landauer-type calculations are often found to describe measurement results better despite the large electron-electron interactions in QDs. More recently, nonlinear thermoelectric effects have moved into the focus of attention and we offer a brief overview of experiments done so far. We conclude by discussing open questions and avenues for future work, including the role of asymmetries in tunnel- and capacitive couplings in thermoelectric behavior of QDs.
    • Artis Svilans, Martin Leijnse, Heiner Linke
      Journal reference: Comptes rendus - Physique 17 (2016) pp. 1096-1108 [pdf]
      DOI: 10.1016/j.crhy.2016.08.002

    • Electron-hole interactions in coupled InAs-GaSb quantum dots based on nanowire crystal phase templates - Abstract
      • We report growth and characterization of a coupled quantum dot structure that utilizes nanowire templates for selective epitaxy of radial heterostructures. The starting point is a zinc blende InAs nanowire with thin segments of wurtzite structure. These segments have dual roles: they act as tunnel barriers for electron transport in the InAs core, and they also locally suppress growth of a GaSb shell, resulting in coaxial InAs-GaSb quantum dots with integrated electrical probes. The parallel quantum dot structure hosts spatially separated electrons and holes that interact due to the type-II broken gap of InAs-GaSb heterojunctions. The Coulomb blockade in the electron and hole transport is studied, and periodic interactions of electrons and holes are observed and can be reproduced by modeling. Distorted Coulomb diamonds indicate voltage-induced ground-state transitions, possibly a result of changes in the spatial distribution of holes in the thin GaSb shell.
    • Malin Nilsson, Luna Namazi, Sebastian Lehmann, Martin Leijnse, Kimberly A. Dick, Claes Thelander
      Journal reference: Phys. Rev. B 94, 115313 (2016) [pdf]
      DOI: 10.1103/PhysRevB.94.115313

    • Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires - Abstract
      • We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating inter-island Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a regime of four Majorana bound states allowing for topologically protected Majorana manipulations. From the energy spectrum, we derive conservative estimates for the time scales of a fusion-rule testing protocol proposed recently [arXiv:1511.05153]. We also analyze the steps needed for basic Majorana braiding operations in branched nanowire structures.
    • Michael Hell, Jeroen Danon, Karsten Flensberg, Martin Leijnse
      Journal reference: Phys. Rev. B 94, 035424 (2016) [pdf]
      DOI: 10.1103/PhysRevB.94.035424

    • Nonlinear thermoelectric efficiency of superlattice-structured nanowires - Abstract
      • We theoretically investigate nonlinear ballistic thermoelectric transport in a superlattice-structured nanowire. By a special choice of nonuniform widths of the superlattice barriers - analogous to anti-reflection coating in optical systems - it is possible to achieve a transmission which comes close to a square profile as a function of energy. We calculate the low-temperature output power and power-conversion efficiency of a thermoelectric generator based on such a structure and show that the efficiency remains high also when operating at a significant power. To provide guidelines for experiments, we study how the results depend on the nanowire radius, the number of barriers, and on random imperfections in barrier width and separation. Our results indicate that high efficiencies can indeed be achieved with todays capabilities in epitaxial nanowire growth.
    • Hossein Karbaschi, John Lovén, Klara Courteaut, Andreas Wacker, Martin Leijnse
      Journal reference: Phys. Rev. B 94, 115414 (2016) [pdf]
      DOI: 10.1103/PhysRevB.94.115414

    • Single-electron transport in InAs nanowire quantum dots formed by crystal phase engineering - Abstract
      • We report electrical characterization of quantum dots formed by introducing pairs of thin wurtzite (WZ) segments in zinc blende (ZB) InAs nanowires. Regular Coulomb oscillations are observed over a wide gate voltage span, indicating that WZ segments create significant barriers for electron transport. We find a direct correlation of transport properties with quantum dot length and corresponding growth time of the enclosed ZB segment. The correlation is made possible by using a method to extract lengths of nanowire crystal phase segments directly from scanning electron microscopy images, and with support from transmission electron microscope images of typical nanowires. From experiments on controlled filling of nearly empty dots with electrons, up to the point where Coulomb oscillations can no longer be resolved, we estimate a lower bound for the ZB-WZ conduction-band offset of 95 meV.
    • Malin Nilsson, Luna Namazi, Sebastian Lehmann, Martin Leijnse, Kimberly A. Dick, Claes Thelander
      Journal reference: Phys. Rev. B 93, 195422 (2016) [pdf]
      DOI: 10.1103/PhysRevB.93.195422

    • Milestones Toward Majorana-Based Quantum Computing - Abstract
      • We introduce a scheme for preparation, manipulation, and readout of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate-control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current; (2) validation of a prototype topological qubit; and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and readout schemes as well.
    • David Aasen, Michael Hell, Ryan V. Mishmash, Andrew Higginbotham, Jeroen Danon, Martin Leijnse, Thomas S. Jespersen, Joshua A. Folk, Charles M. Marcus, Karsten Flensberg, Jason Alicea
      Journal reference: Phys. Rev. X 6, 031016 (2016) [pdf]
      DOI: 10.1103/PhysRevX.6.031016

  • 2015
    • Spin resonance without spin splitting - Abstract
      • We predict that a single-level quantum dot without discernible splitting of its spin states develops a spin-precession resonance in charge transport when embedded into a spin valve. The resonance occurs in the generic situation of Coulomb blockaded transport with ferromagnetic leads whose polarizations deviate from perfect antiparallel alignment. The resonance appears when electrically tuning the interaction-induced exchange field perpendicular to one of the polarizations -- a simple condition relying on vectors in contrast to usual resonance conditions associated with energy splittings. The spin resonance can be detected by stationary dI/dV spectroscopy and by oscillations in the time-averaged current using a gate-pulsing scheme. The generic noncollinearity of the ferromagnets and junction asymmetry allow for an all-electric determination of the spin-injection asymmetry, the anisotropy of spin relaxation, and the magnitude of the exchange field. We also investigate the impact of a nearby superconductor on the resonance position. Our simplistic model turns out to be generic for a broad class of coherent few-level quantum systems.
    • M. Hell, B. Sothmann, M. Leijnse, M. R. Wegewijs, J. König
      Journal reference: Phys. Rev. B 91, 195404 (2015) [pdf]
      DOI: 10.1103/PhysRevB.91.195404

    • Probing transverse magnetic anisotropy by electronic transport through a single-molecule magnet - Abstract
      • By means of electronic transport, we study the transverse magnetic anisotropy of an individual Fe$_4$ single-molecule magnet (SMM) embedded in a three-terminal junction. In particular, we determine in situ the transverse anisotropy of the molecule from the pronounced intensity modulations of the linear conductance, which are observed as a function of applied magnetic field. The proposed technique works at temperatures exceeding the energy scale of the tunnel splittings of the SMM. We deduce that the transverse anisotropy for a single Fe$_4$ molecule captured in a junction is substantially larger than the bulk value.
    • M. Misiorny, E. Burzurí, R. Gaudenzi, K. Park, M. Leijnse, M. R. Wegewijs, J. Paaske, A. Cornia, H. S. J. van der Zant
      Journal reference: Physical Review B 91, 035442 (2015) [pdf]
      DOI: 10.1103/PhysRevB.91.035442

    • Nonlinear thermoelectric response due to energy-dependent transport properties of a quantum dot - Abstract
      • Quantum dots are useful model systems for studying quantum thermoelectric behavior because of their highly energy-dependent electron transport properties, which are tunable by electrostatic gating. As a result of this strong energy dependence, the thermoelectric response of quantum dots is expected to be nonlinear with respect to an applied thermal bias. However, until now this effect has been challenging to observe because, first, it is experimentally difficult to apply a sufficiently large thermal bias at the nanoscale and, second, it is difficult to distinguish thermal bias effects from purely temperature-dependent effects due to overall heating of a device. Here we take advantage of a novel thermal biasing technique and demonstrate a nonlinear thermoelectric response in a quantum dot which is defined in a heterostructured semiconductor nanowire. We also show that a theoretical model based on the Master equations fully explains the observed nonlinear thermoelectric response given the energy-dependent transport properties of the quantum dot.
    • Artis Svilans, Adam M. Burke, Sofia Fahlvik Svensson, Martin Leijnse, Heiner Linke
      Journal reference: Physica E 82 (2015) 34-38 [pdf]
      DOI: 10.1016/j.physe.2015.10.007

    • Transport studies of electron-hole and spin-orbit interaction in GaSb/InAsSb core-shell nanowire quantum dots - Abstract
      • We report low-temperature transport studies of parallel double quantum dots formed in GaSb/InAsSb core-shell nanowires. At negative gate voltages, regular patterns of Coulomb diamonds are observed in the charge stability diagrams, which we ascribe to single-hole tunneling through a quantum dot in the GaSb core. As the gate voltage increases, the measured charge stability diagram indicates the appearance of an additional quantum dot, which we suggest is an electron quantum dot formed in the InAsSb shell. We find that an electron-hole interaction induces shifts of transport resonances in the source-drain voltage from which an average electron-hole interaction strength of 2.9 meV is extracted. We also carry out magnetotransport measurements of a hole quantum dot in the GaSb core and extract level-dependent g- factors and a spin-orbit interaction.
    • Bahram Ganjipour, Martin Leijnse, Lars Samuelson, H. Q. Xu, Claes Thelander
      Journal reference: Physical Review B 91, 161301(R) (2015) [pdf]
      DOI: 10.1103/PhysRevB.91.161301

    • Thermoelectric performance of classical topological insulator nanowires - Abstract
      • There is currently substantial effort being invested into creating efficient thermoelectric nanowires based on topological insulator chalcogenide-type materials. A key premise of these efforts is the assumption that the generally good thermoelectric properties that these materials exhibit in bulk form will translate into similarly good or even better thermoelectric performance of the same materials in nanowire form. Here, we calculate thermoelectric performance of topological insulator nanowires based on Bi2Te3, Sb2Te3 and Bi2Se3 as a function of diameter and Fermi level. We show that the thermoelectric performance of topological insulator nanowires does not derive from the properties of the bulk material in a straightforward way. For all investigated systems the competition between surface states and bulk channel causes a significant modification of the thermoelectric transport coefficients if the diameter is reduced into the sub-10 um range. Key aspects are that the surface and bulk states are optimized at different Fermi levels or have different polarity as well as the high surface to volume ratio of the nanowires. This limits the maximum thermoelectric performance of topological insulator nanowires and thus their application in efficient thermoelectric devices.
    • Johannes Gooth, Jan Goeran Gluschke, Robert Zierold, Martin Leijnse, Heiner Linke, Kornelius Nielsch
      DOI: 10.1088/0268-1242/30/1/015015
      1405.1592v3 [pdf]

  • 2014
    • Tunnel spectroscopy of Majorana bound states in topological superconductor/quantum dot Josephson junctions - Abstract
      • We theoretically investigate electronic transport through a junction where a quantum dot (QD) is tunnel coupled on both sides to semiconductor nanowires with strong spin-orbit interaction and proximity-induced superconductivity. The results are presented as stability diagrams, i.e., the differential conductance as a function of the bias voltage applied across the junction and the gate voltage used to control the electrostatic potential on the QD. A small applied magnetic field splits and modifies the resonances due to the Zeeman splitting of the QD level. Above a critical field strength, Majorana bound states (MBS) appear at the interfaces between the two superconducting nanowires and the QD, resulting in a qualitative change of the entire stability diagram, suggesting this setup as a promising platform to identify MBS. Our calculations are based on a nonequilibrium Green's function description and is exact when Coulomb interactions on the QD can be neglected. In addition, we develop a simple pictorial view of the involved transport processes, which is equivalent to a description in terms of multiple Andreev reflections, but provides an alternative way to understand the role of the QD level in enhancing transport for certain gate and bias voltages. We believe that this description will be useful in future studies of interacting QDs coupled to superconducting leads (with or without MBS), where it can be used to develop a perturbation expansion in the tunnel coupling.
    • Guang-Yao Huang, Martin Leijnse, Karsten Flensberg, Hongqi Xu
      Journal reference: Phys. Rev. B 90, 214507 (2014) [pdf]
      DOI: 10.1103/PhysRevB.90.214507

    • Using Polymer Electrolyte Gates to Set‐and‐Freeze Threshold Voltage and Local Potential in Nanowire‐based Devices and Thermoelectrics - Abstract
      • We use the strongly temperature-dependent ionic mobility in polymer electrolytes to 'freeze in' specific ionic charge environments around a nanowire using a local wrap-gate geometry. This enables us to set both the threshold voltage for a conventional doped substrate gate and the local disorder potential at temperatures below 200 Kelvin, which we characterize in detail by combining conductance and thermovoltage measurements with modeling. Our results demonstrate that local polymer electrolyte gates are compatible with nanowire thermoelectrics, where they offer the advantage of a very low thermal conductivity, and hold great potential towards setting the optimal operating point for solid-state cooling applications.
    • Sofia Fahlvik Svensson, Adam M. Burke, Damon J. Carrad, Martin Leijnse, Heiner Linke, Adam P. Micolich
      DOI: 10.1002/adfm.201402921
      1411.2727v1 [pdf]

    • Designing - Abstract
      • We propose and analyze a new way of using $\pi$ stacking to design molecular junctions that either enhance or suppress a phononic heat current, but at the same time remain conductors for an electric current. Such functionality is highly desirable in thermoelectric energy converters, as well as in other electronic components where heat dissipation should be minimized or maximized. We suggest a molecular design consisting of two masses coupled to each other with one mass coupled to each lead. By having a small coupling (spring constant) between the masses, it is possible to either reduce, or perhaps more surprisingly enhance the phonon conductance. We investigate a simple model system to identify optimal parameter regimes and then use first principle calculations to extract model parameters for a number of specific molecular realizations, confirming that our proposal can indeed be realized using standard molecular building blocks.
    • Gediminas Kiršanskas, Qian Li, Karsten Flensberg, Gemma C. Solomon, Martin Leijnse
      Journal reference: Appl. Phys. Lett. 105, 233102 (2014) [pdf]
      DOI: 10.1063/1.4903340

    • Quantum interference in off-resonant transport through single molecules - Abstract
      • We provide a simple set of rules for predicting interference effects in off-resonant transport through single-molecule junctions. These effects fall in two classes, showing respectively an odd or an even number of nodes in the linear conductance within a given molecular charge state, and we demonstrate how to decide the interference class directly from the contacting geometry. For neutral alternant hydrocarbons, we employ the Coulson-Rushbrooke-McLachlan pairing theorem to show that the interference class is decided simply by tunneling on and off the molecule from same, or different sublattices. More generally, we investigate a range of smaller molecules by means of exact diag- onalization combined with a perturbative treatment of the molecule-lead tunnel coupling. While these results generally agree well with GW calculations, they are shown to be at odds with simpler mean-field treatments. For molecules with spin-degenerate ground states, we show that for most junctions, interference causes no transmission nodes, but argue that it may lead to a non-standard gate-dependence of the zero-bias Kondo resonance.
    • Kim G. L. Pedersen, Mikkel Strange, Martin Leijnse, Per Hedegård, Gemma Solomon, Jens Paaske
      Journal reference: Phys. Rev. B 90, 125413 (2014) [pdf]
      DOI: 10.1103/PhysRevB.90.125413

    • Thermoelectric signatures of a Majorana bound state coupled to a quantum dot - Abstract
      • We theoretically investigate the possibility to use thermolectric measurements to detect Majorana bound states and to investigate their coupling to a dissipative environment. The particle-hole symmetry of Majorana states would normally lead to a vanishing Seebeck coefficient, i.e., a vanishing open-circuit voltage resulting from a temperature gradient. We discuss how coupling to a quantum dot with a gate-controlled energy level breaks particle-hole symmetry in a tunable manner. The resulting gate-dependent Seebeck coefficient provides a new way to evidence the existence of Majorana states, which can be combined with conventional tunnel spectroscopy in the same setup. Furthermore, the thermoelectric properties rely on the ability of the quantum dot-Majorana system to sense the temperature of the bulk superconductor and can be used to extract information about the dissipative decay of Majorana states, which is crucial for quantum information applications.
    • Martin Leijnse
      Journal reference: New J. Phys. 16, 015029 (2014) [pdf]
      DOI: 10.1088/1367-2630/16/1/015029

  • 2013
    • Coupling Spin Qubits via Superconductors - Abstract
      • We show how superconductors can be used to couple, initialize, and read out spatially separated spin qubits. When two single-electron quantum dots are tunnel coupled to the same superconductor, the singlet component of the two-electron state partially leaks into the superconductor via crossed Andreev reflection. This induces a gate-controlled singlet-triplet splitting which, with an appropriate superconductor geometry, remains large for dot separations within the superconducting coherence length. Furthermore, we show that when two double-dot singlet-triplet qubits are tunnel coupled to a superconductor with finite charging energy, crossed Andreev reflection enables a strong two-qubit coupling over distances much larger than the coherence length.
    • Martin Leijnse, Karsten Flensberg
      Journal reference: Phys. Rev. Lett. 111, 060501 (2013) [pdf]
      DOI: 10.1103/PhysRevLett.111.060501

    • Heat, molecular vibrations, and adiabatic driving in non-equilibrium transport through interacting quantum dots - Abstract
      • In this article we review aspects of charge and heat transport in interacting quantum dots and molecular junctions under stationary and time-dependent non-equilibrium conditions due to finite electrical and thermal bias. In particular, we discuss how a discrete level spectrum can be beneficial for thermoelectric applications, and investigate the detrimental effects of molecular vibrations on the efficiency of a molecular quantum dot as an energy converter. In addition, we consider the effects of a slow time-dependent modulation of applied voltages on the transport properties of a quantum dot and show how this can be used as a spectroscopic tool complementary to standard dc-measurements. Finally, we combine time-dependent driving with thermoelectrics in a double-quantum dot system - a nanoscale analogue of a cyclic heat engine - and discuss its operation and the main limitations to its performance.
    • F. Haupt, M. Leijnse, H. L. Calvo, L. Classen, J. Splettstoesser, M. R. Wegewijs
      DOI: 10.1002/pssb.201349219
      1306.4343v1 [pdf]

    • Interaction effects in electric transport through self-assembled molecular monolayers - Abstract
      • We theoretically investigate the effect of inter-molecular Coulomb interactions on transport through molecular monolayers (or other devices based on a large number of nanoscale conductors connected in parallel). Due to the interactions, the current through different molecules become correlated, resulting in distinct features in the non-linear current-voltage characteristics, as we show by deriving and solving a type of modified master equation, suitable for describing transport through an infinite number of interacting conductors. Furthermore, if some of the molecules fail to bond to both electrodes, charge traps can be induced at high voltages and block transport through neighboring molecules, resulting in negative differential resistance.
    • Martin Leijnse
      Journal reference: Phys. Rev. B 87, 125417 (2013) [pdf]
      DOI: 10.1103/PhysRevB.87.125417

  • 2012
    • Manipulation of organic polyradicals in a single-molecule transistor - Abstract
      • Inspired by cotunneling spectroscopy of spin-states in a single OPE5-based molecule, we investigate the prospects for electric control of magnetism in purely organic molecules contacted in a three-terminal geometry. Using the gate electrode, the molecule is reversibly switched between three different redox states, with magnetic spectra revealing both ferromagnetic and antiferromagnetic exchange couplings on the molecule. These observations are shown to be captured by an effective low-energy Heisenberg model, which we substantiate microscopically by a simple valence bond description of the molecule. These preliminary findings suggest an interesting route towards functionalized all-organic molecular magnetism.
    • J. Fock, M. Leijnse, K. Jennum, A. S. Zyazin, J. Paaske, P. Hedegård, M. Brøndsted Nielsen, H. S. J. van der Zant
      Journal reference: Phys. Rev. B 86, 235403 (2012) [5 pages] [pdf]
      DOI: 10.1103/PhysRevB.86.235403

    • Introduction to topological superconductivity and Majorana fermions - Abstract
      • This short review article provides a pedagogical introduction to the rapidly growing research field of Majorana fermions in topological superconductors. We first discuss in some details the simplest "toy model" in which Majoranas appear, namely a one-dimensional tight-binding representation of a p-wave superconductor, introduced more than ten years ago by Kitaev. We then give a general introduction to the remarkable properties of Majorana fermions in condensed matter systems, such as their intrinsically non-local nature and exotic exchange statistics, and explain why these quasiparticles are suspected to be especially well suited for low-decoherence quantum information processing. We also discuss the experimentally promising (and perhaps already successfully realized) possibility of creating topological superconductors using semiconductors with strong spin-orbit coupling, proximity-coupled to standard s-wave superconductors and exposed to a magnetic field. The goal is to provide an introduction to the subject for experimentalists or theorists who are new to the field, focusing on the aspects which are most important for understanding the basic physics. The text should be accessible for readers with a basic understanding of quantum mechanics and second quantization, and does not require knowledge of quantum field theory or topological states of matter.
    • Martin Leijnse, Karsten Flensberg
      Journal reference: Semicond. Sci. Technol. 27, 124003 (2012) [pdf]
      DOI: 10.1088/0268-1242/27/12/124003

    • Parity qubits and poor man's Majorana bound states in double quantum dots - Abstract
      • We study a double quantum dot connected via a common superconducting lead and show that this system can be tuned to host one Majorana bound state (MBS) on each dot. We call them "poor man's Majorana bound states" since they are not topologically protected, but otherwise share the properties of MBS formed in topological superconductors. We describe the conditions for the existence of the two spatially separated MBS, which include breaking of spin degeneracy in the two dots, with the spins polarized in different directions. Therefore, we propose to use a magnetic field configuration where the field directions on the two dot form an angle. By control of this angle the cross Andreev reflection and the tunnel amplitudes can be tuned to be approximately equal, which is a requirement for the formation of the MBS. We show that the fermionic state encoded in the two Majoranas constitutes a parity qubit, which is non-local and can only be measured by probing both dots simultaneously. Using a many-particle basis for the MBS, we discuss the role of interactions and show that inter-dot interactions always lift the degeneracy. We also show how the MBS can be probed by transport measurements and discuss how the combination of several such double dot systems allows for entanglement of parity qubits and measurement of their dephasing times.
    • Martin Leijnse, Karsten Flensberg
      Journal reference: Phys. Rev. B. 86, 134528 (2012) [pdf]
      DOI: 10.1103/PhysRevB.86.134528

    • Finite-bias conductance anomalies at a singlet-triplet crossing - Abstract
      • Quantum dots and single-molecule transistors may exhibit level crossings induced by tuning external parameters such as magnetic field or gate voltage. For Coulomb blockaded devices, this shows up as an inelastic cotunneling threshold in the differential conductance, which can be tuned to zero at the crossing. Here we show that, in addition, level crossings can give rise to a nearly vertical step-edge, ridge or even a Fano-like ridge-valley feature in the differential conductance inside the relevant Coulomb diamond. We study a gate-tunable quasidegeneracy between singlet and triplet ground states, and demonstrate how these different shapes may result from a competition between nonequilibrium occupations and weak (spin-orbit) mixing of the states. Our results are shown to be in qualitative agreement with recent transport measurements on a Mn complex [E. A. Osorio, et al., Nano Lett. 10, 105 (2010)]. The effect remains entirely general and should be observable in a wide range of Coulomb blockaded devices.
    • Chiara Stevanato, Martin Leijnse, Karsten Flensberg, Jens Paaske
      Journal reference: Phys. Rev. B 86, 165427 (2012) [pdf]
      DOI: 10.1103/PhysRevB.86.165427

    • Hybrid topological-spin qubit systems for two-qubit-spin gates - Abstract
      • We investigate a hybrid quantum system involving spin qubits, based on the spins of electrons confined in quantum dots, and topological qubits, based on Majorana fermions. In such a system, gated control of the charge on the quantum dots allows transfer of quantum information between the spin and topological qubits, and the topological system can be used to facilitate transfer of spin qubits between spatially separated quantum dots and to initialize entangled spin-qubit pairs. Here, we show that the coupling to the topological system also makes it possible to perform entangling two-qubit gates on spatially separated spin qubits. The two-qubit gates are based on a combination of topologically protected braiding operations, gate-controlled charge transfer between the dots and edge Majorana modes, and measurements of the state of the topological qubits.
    • Martin Leijnse, Karsten Flensberg
      Journal reference: Phys. Rev. B 86, 104511 (2012) [pdf]
      DOI: 10.1103/PhysRevB.86.104511

    • Parallel carbon nanotube quantum dots and their interactions - Abstract
      • We present quantum transport measurements of interacting parallel quantum dots formed in the strands of a carbon nanotube rope. In this molecular quantum dot system, transport is dominated by one quantum dot, while additional resonances from parallel side dots appear, which exhibit a weak gate coupling. This differential gating effect provides a tunability of the quantum dot system with only one gate electrode and provides control over the carbon nanotube strand that carries the current. By tuning the system to different states we use quantum transport as a spectroscopic tool to investigate the inter-dot coupling and show a route to distinguish between various side dots. By comparing the experimental data with master equation calculations, we identify conditions for the tunneling rates that are required in order to observe different manifestations of the inter-dot coupling in the transport spectra.
    • Karin Goß, Martin Leijnse, Sebastian Smerat, Maarten R. Wegewijs, Claus M. Schneider, Carola Meyer
      DOI: 10.1103/PhysRevB.87.035424
      1208.5860v1 [pdf]

  • 2011
    • Quantum Information Transfer between Topological and Spin Qubit Systems - Abstract
      • We propose a method to coherently transfer quantum information, and to create entanglement, between topological qubits and conventional spin qubits. Our suggestion uses gated control to transfer an electron (spin qubit) between a quantum dot and edge Majorana modes in adjacent topological superconductors. Because of the spin polarization of the Majorana modes, the electron transfer translates spin superposition states into superposition states of the Majorana system, and vice versa. Furthermore, we show how a topological superconductor can be used to facilitate long-distance quantum information transfer and entanglement between spatially separated spin qubits.
    • Martin Leijnse, Karsten Flensberg
      Journal reference: Phys. Rev. Lett. 107, 210502 (2011) [pdf]
      DOI: 10.1103/PhysRevLett.107.210502

    • Scheme to measure Majorana fermion lifetimes using a quantum dot - Abstract
      • We propose a setup to measure the lifetime of the parity of a pair of Majorana bound states. The proposed experiment has one edge Majorana state tunnel coupled to a quantum dot, which in turn is coupled to a metallic electrode. When the Majorana Fermions overlap, even a small relaxation rate qualitatively changes the non-linear transport spectrum, and for strong overlap the lifetime can be read off directly from the height of a current peak. This is important for the usage of Majorana Fermions as a platform for topological quantum computing, where the parity relaxation is a limiting factor.
    • Martin Leijnse, Karsten Flensberg
      Journal reference: Phys. Rev. B 84, 140501(R) (2011) [pdf]
      DOI: 10.1103/PhysRevB.84.140501

    • Spin-dependent electronic hybridization in a rope of carbon nanotubes - Abstract
      • We demonstrate single electron addition to different strands of a carbon nanotube rope. Anticrossings of anomalous conductance peaks occur in quantum transport measurements through the parallel quantum dots forming on the individual strands. We determine the magnitude and the sign of the hybridization as well as the Coulomb interaction between the carbon nanotube quantum dots, finding that the bonding states dominate the transport. In a magnetic field the hybridization is shown to be selectively suppressed due to spin effects.
    • Karin Goß, Sebastian Smerat, Martin Leijnse, Maarten R. Wegewijs, Claus M. Schneider, Carola Meyer
      Journal reference: Phys. Rev. B 83, 201403(R) (2011) [pdf]
      DOI: 10.1103/PhysRevB.83.201403

    • Interaction-induced negative differential resistance in asymmetric molecular junctions - Abstract
      • Combining insights from quantum chemistry calculations with master equations, we discuss a mechanism for negative differential resistance (NDR) in molecular junctions, operated in the regime of weak tunnel coupling. The NDR originates from an interplay of orbital spatial asymmetry and strong electron-electron interaction, which causes the molecule to become trapped in a non-conducting state above a voltage threshold. We show how the desired asymmetry can be selectively introduced in individual orbitals in e.g., OPE-type molecules by functionalization with a suitable side group, which is in linear conjugation to one end of the molecule and cross-conjugated to the other end.
    • Martin Leijnse, Wei Sun, Mogens Brøndsted Nielsen, Per Hedegård, Karsten Flensberg
      Journal reference: J. Chem. Phys. 134, 104107 (2011) [pdf]
      DOI: 10.1063/1.3560474

  • 2010
    • Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory - Abstract
      • Various theoretical methods address transport effects in quantum dots beyond single-electron tunneling while accounting for the strong interactions in such systems. In this paper we report a detailed comparison between three prominent approaches to quantum transport: the fourth-order Bloch-Redfield quantum master equation (BR), the real-time diagrammatic technique (RT), and the scattering rate approach based on the T-matrix (TM). Central to the BR and RT is the generalized master equation for the reduced density matrix. We demonstrate the exact equivalence of these two techniques. By accounting for coherences (nondiagonal elements of the density matrix) between nonsecular states, we show how contributions to the transport kernels can be grouped in a physically meaningful way. This not only significantly reduces the numerical cost of evaluating the kernels but also yields expressions similar to those obtained in the TM approach, allowing for a detailed comparison. However, in the TM approach an ad hoc regularization procedure is required to cure spurious divergences in the expressions for the transition rates in the stationary (zero-frequency) limit. We show that these problems derive from incomplete cancellation of reducible contributions and do not occur in the BR and RT techniques, resulting in well-behaved expressions in the latter two cases. Additionally, we show that a standard regularization procedure of the TM rates employed in the literature does not correctly reproduce the BR and RT expressions. All the results apply to general quantum dot models and we present explicit rules for the simplified calculation of the zero-frequency kernels. Although we focus on fourth-order perturbation theory only, the results and implications generalize to higher orders. We illustrate our findings for the single impurity Anderson model with finite Coulomb interaction in a magnetic field.
    • Sonja Koller, Martin Leijnse, Maarten R. Wegewijs, Milena Grifoni
      Journal reference: Phys. Rev. B 82, 235307 (2010) [pdf]
      DOI: 10.1103/PhysRevB.82.235307

    • Electric Field Controlled Magnetic Anisotropy in a Single Molecule - Abstract
      • We have measured quantum transport through an individual Fe$_4$ single-molecule magnet embedded in a three-terminal device geometry. The characteristic zero-field splittings of adjacent charge states and their magnetic field evolution are observed in inelastic tunneling spectroscopy. We demonstrate that the molecule retains its magnetic properties, and moreover, that the magnetic anisotropy is significantly enhanced by reversible electron addition / subtraction controlled with the gate voltage. Single-molecule magnetism can thus be electrically controlled.
    • Alexander S. Zyazin, Johan W. G. van den Berg, Edgar A. Osorio, Herre S. J. van der Zant, Nikolaos P. Konstantinidis, Martin Leijnse, Maarten R. Wegewijs, Falk May, Walter Hofstetter, Chiara Danieli, Andrea Cornia
      Journal reference: Nano Lett. 10, 3307 (2010) [pdf]
      DOI: 10.1021/nl1009603

    • Nonlinear thermoelectric properties of molecular junctions with vibrational coupling - Abstract
      • We present a detailed study of the non-linear thermoelectric properties of a molecular junction, represented by a dissipative Anderson-Holstein model. A single orbital level with strong Coulomb interaction is coupled to a localized vibrational mode and we account for both electron and phonon exchange with both electrodes, investigating how these contribute to the heat and charge transport. We calculate the efficiency and power output of the device operated as a heat to electric power converter and identify the optimal operating conditions, which are found to be qualitatively changed by the presence of the vibrational mode. Based on this study of a generic model system, we discuss the desirable properties of molecular junctions for thermoelectric applications.
    • M. Leijnse, M. R. Wegewijs, K. Flensberg
      Journal reference: Phys. Rev. B 82, 045412 (2010) [pdf]
      DOI: 10.1103/PhysRevB.82.045412

    • Transport via coupled states in a - Abstract
      • We have measured systematic repetitions of avoided crossings in low temperature three-terminal transport through a carbon nanotube with encapsulated C60 molecules. We show that this is a general effect of the hybridization of a host quantum dot with an impurity. The well-defined nanotube allows identification of the properties of the impurity, which we suggest to be a chain of C60 molecules inside the nanotube. This electronic coupling between the two subsystems opens the interesting and potentially useful possibility of contacting the encapsulated molecules via the tube.
    • Anders Eliasen, Jens Paaske, Karsten Flensberg, Sebastian Smerat, Martin Leijnse, Maarten R. Wegewijs, Henrik I. Jørgensen, Marc Monthioux, Jesper Nygård
      DOI: 10.1103/PhysRevB.81.155431
      1002.0477v1 [pdf]

  • 2009
    • Pair Tunneling Resonance in the Single-Electron Transport Regime - Abstract
      • We predict a new electron pair-tunneling (PT) resonance in non-linear transport through quantum dots with positive charging energies exceeding the broadening due to thermal and quantum fluctuations. The PT resonance shows up in the single-electron transport (SET) regime as a peak in the derivative of the non-linear conductance when the electrochemical potential of one electrode matches the average of two subsequent charge addition energies. For a single level quantum dot (Anderson model) we find the analytic peak shape and the dependence on temperature, magnetic field and junction asymmetry and compare with the inelastic cotunneling peak which is of the same order of magnitude. In experimental transport data the PT resonance may be mistaken for a weak SET resonance judging only by the voltage dependence of its position. Our results provide essential clues to avoid such erroneous interpretation of transport spectroscopy data.
    • M. Leijnse, M. R. Wegewijs, M. H. Hettler
      Journal reference: Phys. Rev. Lett. 103, 156803 (2009) [pdf]
      DOI: 10.1103/PhysRevLett.103.156803

    • Pumping of Vibrational Excitations in the Coulomb-Blockade Regime in a Suspended Carbon Nanotube - Abstract
      • Low-temperature transport spectroscopy measurements on a suspended few-hole carbon nanotube quantum dot are presented, showing a gate-dependent harmonic excitation spectrum which, strikingly, occurs in the Coulomb blockade regime. The quantized excitation energy corresponds to the scale expected for longitudinal vibrations of the nanotube. The electronic transport processes are identified as cotunnel-assisted sequential tunneling, resulting from non-equilibrium occupation of the mechanical mode. They appear only above a high-bias threshold at the scale of electronic nanotube excitations. We discuss models for the pumping process that explain the enhancement of the non-equilibrium occupation and show that it is connected to a subtle interplay between electronic and vibrational degrees of freedom.
    • A. K. Huettel, B. Witkamp, M. Leijnse, M. R. Wegewijs, H. S. J. van der Zant
      Journal reference: Phys. Rev. Lett. 102, 225501 (2009) [pdf]
      DOI: 10.1103/PhysRevLett.102.225501

    • Vibrational detection and control of spin in mixed-valence molecular transistors - Abstract
      • We investigate electron transport through a mixed-valence molecular complex in which an excess electron can tunnel between hetero-valent transition metal ions, each having a fixed localized spin. We show that in this class of molecules the interplay of the spins and the vibrational breathing modes of the ionic ligand-shells allows the total molecular spin to be detected as well as controlled by nonequilibrium transport. Due to a spin-dependent pseudo Jahn-Teller effect electronic transitions with different spin values can be distinguished by their vibronic conductance side peaks, without using an external magnetic field. Conversely, we show that the spin state of the entire molecule can also be controlled via the nonequilibrium quantized molecular vibrations due to a vibration-induced spin-blockade.
    • F. Reckermann, M. Leijnse, M. R. Wegewijs
      Journal reference: Physical Review B 79, 075313 (2009) [pdf]
      DOI: 10.1103/PhysRevB.79.075313

  • 2008
    • Transport signature of pseudo Jahn-Teller dynamics in a single-molecule transistor - Abstract
      • We calculate the electronic transport through a molecular dimer, in which an excess electron is delocalized over equivalent monomers, which can be locally distorted. In this system the Born-Oppenheimer approximation breaks down resulting in quantum entanglement of the mechanical and electronic motion. We show that pseudo Jahn-Teller (pJT) dynamics of the molecule gives rise to conductance peaks that indicate this violation. Their magnitude, sign and position sharply depend on the electro-mechanical properties of the molecule, which can be varied in recently developed three-terminal junctions with mechanical control. The predicted effect depends crucially on the degree of intramolecular delocalization of the excess electron, a parameter which is also of fundamental importance in physical chemistry.
    • F. Reckermann, M. Leijnse, M. R. Wegewijs, H. Schoeller
      Journal reference: EPL, 83 (2008) 58001 [pdf]
      DOI: 10.1209/0295-5075/83/58001

    • Kinetic equations for transport through single-molecule transistors - Abstract
      • We present explicit kinetic equations for quantum transport through a general molecular quantum-dot, accounting for all contributions up to 4th order perturbation theory in the tunneling Hamiltonian and the complete molecular density matrix. Such a full treatment describes not only sequential, cotunneling and pair tunneling, but also contains terms contributing to renormalization of the molecular resonances as well as their broadening. Due to the latter all terms in the perturbation expansion are automatically well-defined for any set of system parameters, no divergences occur and no by-hand regularization is required. Additionally we show that, in contrast to 2nd order perturbation theory, in 4th order it is essential to account for quantum coherence between non-degenerate states, entering the theory through the non-diagonal elements of the density matrix. As a first application, we study a single-molecule transistor coupled to a localized vibrational mode (Anderson-Holstein model). We find that cotunneling-assisted sequential tunneling processes involving the vibration give rise to current peaks i.e. negative differential conductance in the Coulomb-blockade regime. Such peaks occur in the cross-over to strong electron-vibration coupling, where inelastic cotunneling competes with Franck-Condon suppressed sequential tunneling, and thereby indicate the strength of the electron-vibration coupling. The peaks depend sensitively on the coupling to a dissipative bath, thus providing also an experimental probe of the Q-factor of the vibrational motion.
    • M. Leijnse, M. R. Wegewijs
      Journal reference: Phys. Rev. B 78, 235424 (2008) [pdf]
      DOI: 10.1103/PhysRevB.78.235424