Publications by Jens Paaske

  • 2024
    • BCS surrogate models for floating superconductor-semiconductor hybrids - Abstract
      • Superconductor-semiconductor hybrid devices, involving quantum dots interfaced with floating and/or grounded superconductors, have reached a level of complexity which calls for the development of versatile and numerically efficient modelling tools. Here, we propose an extension of the surrogate model solver for sub-gap states [Phys. Rev. B 108, L220506 (2023)], which is able to handle floating superconducting islands with finite charging energy. Upon eliminating all finite-size effects of the computationally demanding Richardson model approach, we achieve a more efficient way of calculating the sub-gap spectra and related observables without compromising their accuracy. We provide a number of benchmarks between the two approaches and showcase the versatility of the extended surrogate model solver by studying the stability of spin-triplet ground states in various tunable devices. The methods introduced here set the stage for reliable microscopic simulations of complex superconducting quantum circuits across all their relevant parameter regimes.
    • 2402.18357v2 [pdf]
      Virgil V. Baran, Jens Paaske

    • Spin-1 Haldane chains of superconductor-semiconductor hybrids - Abstract
      • We theoretically explore the possibility of realizing the symmetry-protected topological Haldane phase of spin-1 chains in a tunable hybrid platform of superconducting islands (SIs) and quantum dots (QDs). Inspired by recent findings suggesting that an appropriately tuned QD-SI-QD block may behave as a robust spin-1 unit, we study the behavior of many such units tunnel-coupled into linear chains. Our efficient and fully microscopic modeling of long chains with several tens of units is enabled by the use of the surrogate model solver [Phys. Rev. B 108, L220506 (2023); arXiv:2402.18357]. Our numerical findings indicate that the QD-SI-QD chains exhibit emblematic features of the Haldane phase, such as fractional spin-1/2 edge states and non-vanishing string order parameters, and that these persist over a sizeable region of parameter space.
    • 2404.12207v2 [pdf]
      Virgil V. Baran, Jens Paaske

  • 2023
    • Surrogate model solver for impurity-induced superconducting subgap states - Abstract
      • A simple impurity solver is shown to capture the impurity-induced superconducting subgap states in quantitative agreement with the numerical renormalization group and quantum Monte-Carlo simulations. The solver is based on the exact diagonalization of a single-impurity Anderson model with discretized superconducting reservoirs including only a small number of effective levels. Their energies and couplings to the impurity $d$-level are chosen so as to best reproduce the Matsubara frequency dependence of the hybridization function. We provide a number of critical benchmarks and demonstrate the solvers efficiency in combination with the reduced basis method [Phys. Rev. B 107, 144503 (2023)] by calculating the phase diagram for an interacting three-terminal junction.
    • Virgil V. Baran, Emil J. P. Frost, Jens Paaske
      Journal reference: Phys. Rev. B 108, L220506 (2023) [pdf]
      DOI: 10.1103/PhysRevB.108.L220506

  • 2021
    • Inductive microwave response of Yu-Shiba-Rusinov states - Abstract
      • We calculate the frequency-dependent admittance of a phase-biased Josephson junction spanning a magnetic impurity or a spinful Coulomb-blockaded quantum dot. The local magnetic moment gives rise to Yu-Shiba-Rusinov bound states, which govern the sub-gap absorption as well as the inductive response. We model the system by a superconducting spin-polarized exchange-cotunnel junction and calculate the linear current response to an AC bias voltage, including its dependence on phase bias as well as particle-hole, and source-drain coupling asymmetry. The corresponding inductive admittance is analyzed and compared to results of a zero-bandwidth, as well as an infinite-gap approximation to the superconducting Anderson model. All three approaches capture the interaction-induced $0-\pi$ transition, which is reflected as a discontinuity in the adiabatic inductive response.
    • Cecilie Hermansen, Alfredo Levy Yeyati, Jens Paaske
      DOI: 10.1103/PhysRevB.105.054503
      2112.11261v1 [pdf]

    • Direct transport between superconducting subgap states in a double quantum dot - Abstract
      • We demonstrate direct transport between two opposing sets of Yu-Shiba-Rusinov (YSR) subgap states realized in a double quantum dot. This sub-gap transport relies on intrinsic quasiparticle relaxation, but the tunability of the device allows us to explore also an additional relaxation mechanism based on charge transferring Andreev reflections. The transition between these two relaxation regimes is identified in the experiment as a marked gate-induced stepwise change in conductance. We present a transport calculation, including YSR bound states and multiple Andreev reflections alongside with quasiparticle relaxation, due to a weak tunnel coupling to a nearby normal metal, and obtain excellent agreement with the data.
    • Gorm Ole Steffensen, Juan Carlos Estrada Saldaña, Alexandros Vekris, Peter Krogstrup, Kasper Grove-Rasmussen, Jesper Nygård, Alfredo Levy Yeyati, Jens Paaske
      DOI: 10.1103/PhysRevB.105.L161302
      2105.06815v1 [pdf]

    • Spatially dispersing Yu-Shiba-Rusinov states in the unconventional superconductor FeTe0.55Se0.45 - Abstract
      • By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor $\mathrm{FeTe}_{0.55}\mathrm{Se}_{0.45}$, a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tip-sample distance. We find that the impurity state is of the Yu-Shiba-Rusinov (YSR) type, and argue that the energy shift is caused by the low superfluid density in $\mathrm{FeTe}_{0.55}\mathrm{Se}_{0.45}$, which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tip-gating scenario within the single-impurity Anderson model and find good agreement to the experimental data.
    • Damianos Chatzopoulos, Doohee Cho, Koen M. Bastiaans, Gorm O. Steffensen, Damian Bouwmeester, Alireza Akbari, Genda Gu, Jens Paaske, Brian M. Andersen, Milan P. Allan
      Journal reference: Nature Communications 12, 298 (2021) [pdf]
      DOI: 10.1038/s41467-020-20529-x

  • 2020
    • Two-impurity Yu-Shiba-Rusinov states in coupled quantum dots - Abstract
      • Using double quantum dots as the weak link of a Josephson junction, we realize the superconducting analog of the celebrated two-impurity Kondo model. The device shows a cusped current-voltage characteristic, which can be modelled by an overdamped circuit relating the observed cusp current to the Josephson critical current. The gate dependence of the cusp current and of the subgap spectra are used as complementary ground-state indicators to demonstrate gate-tuned changes of the ground state from an inter-dot singlet to independently screened Yu-Shiba-Rusinov (YSR) singlets. In contrast to the two-impurity Kondo effect in normal-state systems, the crossover between these two singlets is heralded by quantum phase boundaries to nearby doublet YSR phases in which only a single spin is screened.
    • J. C. Estrada Saldaña, A. Vekris, R. Žitko, G. Steffensen, P. Krogstrup, J. Paaske, K. Grove-Rasmussen, J. Nygård
      Journal reference: Physical Review B 102, 195143 (2020) [pdf]
      DOI: 10.1103/PhysRevB.102.195143

  • 2019
    • Current-Induced Gap Opening in Interacting Topological Insulator Surfaces - Abstract
      • Two-dimensional topological insulators (TIs) host gapless helical edge states that are predicted to support a quantized two-terminal conductance. Quantization is protected by time-reversal symmetry, which forbids elastic backscattering. Paradoxically, the current-carrying state itself breaks the time-reversal symmetry that protects it. Here we show that the combination of electron-electron interactions and momentum-dependent spin polarization in helical edge states gives rise to feedback through which an applied current opens a gap in the edge state dispersion, thereby breaking the protection against elastic backscattering. Current-induced gap opening is manifested via a nonlinear contribution to the system's $I-V$ characteristic, which persists down to zero temperature. We discuss prospects for realizations in recently discovered large bulk band gap TIs, and an analogous current-induced gap opening mechanism for the surface states of three-dimensional TIs.
    • Ajit C. Balram, Karsten Flensberg, Jens Paaske, Mark S. Rudner
      Journal reference: Phys. Rev. Lett. 123, 246803 (2019) [pdf]
      DOI: 10.1103/PhysRevLett.123.246803

    • The antiferromagnetic phase of the Floquet-driven Hubbard model - Abstract
      • A saddle point plus fluctuations analysis of the periodically driven half-filled two-dimensional Hubbard model is performed. For drive frequencies below the equilibrium gap, we find discontinuous transitions to time-dependent solutions. A highly excited, generically non-thermal distribution of magnons occurs even for drive frequencies far above the gap. Above a critical drive amplitude, the low-energy magnon distribution diverges as the frequency tends to zero and antiferromagnetism is destroyed, revealing the generic importance of collective mode excitations arising from a non-equilibrium drive.
    • Nicklas Walldorf, Dante M. Kennes, Jens Paaske, Andrew J. Millis
      Journal reference: Phys. Rev. B 100, 121110 (2019) [pdf]
      DOI: 10.1103/PhysRevB.100.121110

    • Interplay between magnetic and vestigial nematic orders in the layered - Abstract
      • We study the layered $J_1$-$J_2$ classical Heisenberg model on the square lattice using a self-consistent bond theory. We derive the phase diagram for fixed $J_1$ as a function of temperature $T$, $J_2$ and interplane coupling $J_z$. Broad regions of (anti)ferromagnetic and stripe order are found, and are separated by a first-order transition near $J_2\approx 0.5$ (in units of $|J_1|$). Within the stripe phase the magnetic and vestigial nematic transitions occur simultaneously in first-order fashion for strong $J_z$. For weaker $J_z$ there is in addition, for $J_2^*<j_2 <="<" j_2^{**}$,="J_2^{**}$," an="an" intermediate="intermediate" regime="regime" of="of" split="split" transitions="transitions" implying="implying" a="a" finite="finite" temperature="temperature" region="region" with="with" nematic="nematic" order="order" but="but" no="no" long-range="long-range" stripe="stripe" magnetic="magnetic" order.="order." in="In" this="this" split="split" regime,="regime," the="the" order="order" of="of" the="the" transitions="transitions" depends="depends" sensitively="sensitively" on="on" the="the" deviation="deviation" from="from" $j_2^*$="$J_2^*$" and="and" $j_2^{**}$,="$J_2^{**}$," with="with" split="split" second-order="second-order" transitions="transitions" predominating="predominating" for="for" $j_2^*="$J_2^*" \ll="\ll" j_2="J_2" \ll="\ll" j_2^{**}$.="J_2^{**}$." we="We" find="find" that="that" the="the" value="value" of="of" $j_2^*$="$J_2^*$" depends="depends" weakly="weakly" on="on" the="the" interplane="interplane" coupling="coupling" and="and" is="is" just="just" slightly="slightly" larger="larger" than="than" $0.5$="$0.5$" for="for" $|j_z|="$|J_z|" \lesssim="\lesssim" 0.01$.="0.01$." in="In" contrast="contrast" the="the" value="value" of="of" $j_2^{**}$="$J_2^{**}$" increases="increases" quickly="quickly" from="from" $j_2^*$="$J_2^*$" at="at" $|j_z|="$|J_z|" \lesssim="\lesssim" 0.01$="0.01$" as="as" the="the" interplane="interplane" coupling="coupling" is="is" further="further" reduced.="reduced." in="In" addition,="addition," the="the" magnetic="magnetic" correlation="correlation" length="length" is="is" shown="shown" to="to" directly="directly" depend="depend" on="on" the="the" nematic="nematic" order="order" parameter="parameter" and="and" thus="thus" exhibits="exhibits" a="a" sharp="sharp" increase="increase" (or="(or" jump)="jump)" upon="upon" entering="entering" the="the" nematic="nematic" phase.="phase." our="Our" results="results" are="are" broadly="broadly" consistent="consistent" with="with" predictions="predictions" based="based" on="on" itinerant="itinerant" electron="electron" models="models" of="of" the="the" iron-based="iron-based" superconductors="superconductors" in="In" the="the" normal-state,="normal-state," and="and" thus="thus" help="help" substantiate="substantiate" a="a" classical="classical" spin="spin" framework="framework" for="for" providing="providing" a="a" phenomenological="phenomenological" description="description" of="of" their="their" magnetic="magnetic" properties.
    • Olav F. Syljuåsen, Jens Paaske, Michael Schecter
      Journal reference: Phys. Rev. B 99, 174404 (2019) [pdf]
      DOI: 10.1103/PhysRevB.99.174404

  • 2018
    • Supercurrent in a Double Quantum Dot - Abstract
      • We demonstrate the Josephson effect in a serial double quantum dot defined in a nanowire with epitaxial superconducting leads. The supercurrent stability diagram adopts a honeycomb pattern with electron-hole and left-right reflection symmetry. We observe sharp discontinuities in the magnitude of the critical current, $I_c$, as a function of dot occupation, related to doublet to singlet ground state transitions. Detuning of the energy levels offers a tuning knob for $I_c$, which attains a maximum at zero detuning. The consistency between experiment and theory indicates that our device is a faithful realization of the two-impurity Anderson model.
    • J. C. Estrada Saldaña, A. Vekris, G. Steffensen, R. Žitko, P. Krogstrup, J. Paaske, K. Grove-Rasmussen, J. Nygård
      Journal reference: Phys. Rev. Lett. 121, 257701 (2018) [pdf]
      DOI: 10.1103/PhysRevLett.121.257701

    • Strain-enhanced optical absorbance of topological insulator films - Abstract
      • Topological insulator films are promising materials for optoelectronics due to a strong optical absorption and a thickness dependent band gap of the topological surface states. They are superior candidates for photodetector applications in the THz-infrared spectrum, with a potential performance higher than graphene. Using a first-principles $k\cdot p$ Hamiltonian, incorporating all symmetry-allowed terms to second order in the wave vector $k$, first order in the strain $\epsilon$ and of order $\epsilon k$, we demonstrate significantly improved optoelectronic performance due to strain. For Bi$_2$Se$_3$ films of variable thickness, the surface state band gap, and thereby the optical absorption, can be effectively tuned by application of uniaxial strain, $\epsilon_{zz}$, leading to a divergent band edge absorbance for $\epsilon_{zz}\gtrsim 6\%$. Shear strain breaks the crystal symmetry and leads to an absorbance varying significantly with polarization direction. Remarkably, the directional average of the absorbance always increases with strain, independent of material parameters.
    • Mathias Rosdahl Brems, Jens Paaske, Anders Mathias Lunde, Morten Willatzen
      Journal reference: Phys. Rev. B 97, 081402(R) (2018) [pdf]
      DOI: 10.1103/PhysRevB.97.081402

    • Symmetry analysis of strain, electric and magnetic fields in the Bi - Abstract
      • Based on group theoretical arguments we derive the most general Hamiltonian for the $\text{Bi}_2\text{Se}_3$-class of materials including terms to third order in the wave vector, first order in electric and magnetic fields, first order in strain and first order in both strain and wave vector. We determine analytically the effects of strain on the electronic structure of $\text{Bi}_2\text{Se}_3$. For the most experimentally relevant surface termination we analytically derive the surface state spectrum, revealing an anisotropic Dirac cone with elliptical constant energy counturs giving rise to different velocities in different in-plane directions. The spin-momentum locking of strained $\text{Bi}_2\text{Se}_3$ is shown to be modified and for some strain configurations we see a non-zero spin component perpendicular to the surface. Hence, strain control can be used to manipulate the spin degree of freedom via the spin-orbit coupling. We show that for a thin film of $\text{Bi}_2\text{Se}_3$ the surface state band gap induced by coupling between the opposite surfaces changes opposite to the bulk band gap under strain. Tuning the surface state band gap by strain, gives new possibilities for the experimental investigation of the thickness dependent gap and optimization of optical properties relevant for, e.g., photodetector and energy harvesting applications. We finally derive analytical expressions for the effective mass tensor of the Bi$_2$Se$_3$ class of materials as a function of strain and electric field.
    • Mathias Rosdahl Jensen, Jens Paaske, Anders Mathias Lunde, Morten Willatzen
      Journal reference: New J. Phys. 20 (2018) 053041 [pdf]
      DOI: 10.1088/1367-2630/aabcfc

    • Yu–Shiba–Rusinov screening of spins in double quantum dots - Abstract
      • A magnetic impurity coupled to a superconductor gives rise to a Yu-Shiba-Rusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system switches to a YSR groundstate with bound quasiparticles screening the impurity spin by $\hbar/2$. Here we explore InAs nanowire double quantum dots tunnel coupled to a superconductor and demonstrate YSR screening of spin-1/2 and spin-1 states. Gating the double dot through 9 different charge states, we show that the honeycomb pattern of zero-bias conductance peaks, archetypal of double dots coupled to normal leads, is replaced by lines of zero-energy YSR states. These enclose regions of YSR-screened dot spins displaying distinctive spectral features, and their characteristic shape and topology change markedly with tunnel coupling strengths. We find excellent agreement with a simple zero-bandwidth approximation, and with numerical renormalization group calculations for the two-orbital Anderson model.
    • K. Grove-Rasmussen, G. Steffensen, A. Jellinggaard, M. H. Madsen, R. Žitko, J. Paaske, J. Nygård
      Journal reference: Nature Communications 9, 2376 (2018) [pdf]
      DOI: 10.1038/s41467-018-04683-x

  • 2017
    • Nematic Bond Theory of Heisenberg Helimagnets - Abstract
      • We study classical two-dimensional frustrated Heisenberg models with generically incommensurate groundstates. A new theory for the spin-nematic "order by disorder" transition is developed based on the self-consistent determination of the effective exchange coupling bonds. In our approach, fluctuations of the constraint field imposing conservation of the local magnetic moment drive nematicity at low temperatures. The critical temperature is found to be highly sensitive to the peak helimagnetic wavevector, and vanishes continuously when approaching rotation symmetric Lifshitz points. Transitions between symmetry distinct nematic orders may occur by tuning the exchange parameters, leading to lines of bicritical points.
    • Michael Schecter, Olav. F. Syljuåsen, J. Paaske
      Journal reference: Phys. Rev. Lett. 119, 157202 (2017) [pdf]
      DOI: 10.1103/PhysRevLett.119.157202

    • Kondo blockade due to quantum interference in single-molecule junctions - Abstract
      • Molecular electronics offers unique scientific and technological possibilities, resulting from both the nanometre scale of the devices and their reproducible chemical complexity. Two fundamental yet different effects, with no classical analogue, have been demonstrated experimentally in single-molecule junctions: quantum interference due to competing electron transport pathways, and the Kondo effect due to entanglement from strong electronic interactions. Here we unify these phenomena, showing that transport through a spin-degenerate molecule can be either enhanced or blocked by Kondo correlations, depending on molecular structure, contacting geometry and applied gate voltages. An exact framework is developed, in terms of which the quantum interference properties of interacting molecular junctions can be systematically studied and understood. We prove that an exact Kondo-mediated conductance node results from destructive interference in exchange-cotunneling. Nonstandard temperature dependences and gate-tunable conductance peaks/nodes are demonstrated for prototypical molecular junctions, illustrating the intricate interplay of quantum effects beyond the single-orbital paradigm.
    • Andrew K. Mitchell, Kim G. L. Pedersen, Per Hedegaard, Jens Paaske
      Journal reference: Nature Communications, 8, 15210 (2017) [pdf]
      DOI: 10.1038/ncomms15210

  • 2016
    • Tunable Magnetic Anisotropy from Higher-Harmonics Exchange Scattering on the Surface of a Topological Insulator - Abstract
      • We show that higher-harmonics exchange scattering from a magnetic adatom on the surface of a three dimensional topological insulator leads to a magnetic anisotropy whose magnitude and sign may be tuned by adjusting the chemical potential of the helical surface band. As chemical potential moves from the Dirac point towards the surface band edge, the surface normal is found to change from magnetic easy, to hard axis. Hexagonal warping is shown to diminish the region with easy axis anisotropy, and to suppress the anisotropy altogether. This indirect contribution can be comparable in magnitude to the intrinsic term arising from crystal field splitting and atomic spin-orbit coupling, and its tunability with chemical potential makes the two contributions experimentally discernible, and endows this source of anisotropy with potentially interesting magnetic functionality.
    • Jens Paaske, Erikas Gaidamauskas
      Journal reference: Phys. Rev. Lett. 117, 177201 (2016) [pdf]
      DOI: 10.1103/PhysRevLett.117.177201

    • Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a two-dimensional superconductor - Abstract
      • We study the magnetic and electronic phases of a 1D magnetic adatom chain on a 2D superconductor. In particular, we confirm the existence of a `self-organized' 1D topologically non-trivial superconducting phase within the set of subgap Yu-Shiba-Rusinov (YSR) states formed along the magnetic chain. This phase is stabilized by incommensurate spiral correlations within the magnetic chain that arise from the competition between short-range ferromagnetic and long-range antiferromagnetic electron-induced exchange interactions, similar to a recent study for a 3D superconductor [M. Schecter et al. Phys. Rev. B 93, 140503(R) 2016]. The exchange interaction along diagonal directions are also considered and found to display behavior similar to a 1D substrate when close to half filling. We show that the topological phase diagram is robust against local superconducting order parameter suppression and weak substrate spin-orbit coupling. Lastly, we study the effect of a direct ferromagnetic exchange coupling between the adatoms, and find the region of spiral order in the phase diagram to be significantly enlarged in a wide range of the direct exchange coupling.
    • M. H. Christensen, M. Schecter, K. Flensberg, B. M. Andersen, J. Paaske
      Journal reference: Phys. Rev. B 94, 144509 (2016) [pdf]
      DOI: 10.1103/PhysRevB.94.144509

    • Signatures of Majorana Kramers pairs in superconductor-Luttinger liquid and superconductor-quantum dot-normal lead junctions - Abstract
      • Time-reversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a one-dimensional superconductor is coupled to a normal-metal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electron-electron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquid-Majorana Kramers pair junction and show that its low-energy properties are determined by Andreev reflection scattering processes in the spin-triplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spin-triplet superconductor - normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slave-boson mean-field theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.
    • Younghyun Kim, Dong E. Liu, Erikas Gaidamauskas, Jens Paaske, Karsten Flensberg, Roman M. Lutchyn
      Journal reference: Phys. Rev. B 94, 075439 (2016) [pdf]
      DOI: 10.1103/PhysRevB.94.075439

    • Self-organized topological superconductivity in a Yu-Shiba-Rusinov chain - Abstract
      • We study a chain of magnetic moments exchange coupled to a conventional three dimensional superconductor. In the normal state the chain orders into a collinear configuration, while in the superconducting phase we find that ferromagnetism is unstable to the formation of a magnetic spiral state. Beyond weak exchange coupling the spiral wavevector greatly exceeds the inverse superconducting coherence length as a result of the strong spin-spin interaction mediated through the subgap band of Yu-Shiba-Rusinov states. Moreover, the simple spin-spin exchange description breaks down as the subgap band crosses the Fermi energy, wherein the spiral phase becomes stabilized by the spontaneous opening of a $p-$wave superconducting gap within the band. This leads to the possibility of electron-driven topological superconductivity with Majorana boundary modes using magnetic atoms on superconducting surfaces.
    • M. Schecter, K. Flensberg, M. H. Christensen, B. M. Andersen, J. Paaske
      Journal reference: Phys. Rev. B 93, 140503 (2016) [pdf]
      DOI: 10.1103/PhysRevB.93.140503

  • 2015
    • Yu-Shiba-Rusinov states in phase-biased superconductor–quantum dot–superconductor junctions - Abstract
      • We study the effects of a phase difference on Yu-Shiba-Rusinov (YSR) states in a spinful Coulomb-blockaded quantum dot contacted by a superconducting loop. In the limit where charging energy is larger than the superconducting gap, we determine the subgap excitation spectrum, the corresponding supercurrent, and the differential conductance as measured by a normal-metal tunnel probe. In absence of a phase difference only one linear combination of the superconductor lead electrons couples to the spin, which gives a single YSR state. With finite phase difference, however, it is effectively a two-channel scattering problem and therefore an additional state emerges from the gap edge. The energy of the phase-dependent YSR states depend on the gate voltage and one state can cross zero energy twice inside the valley with odd occupancy. These crossings are shifted by the phase difference towards the charge degeneracy points, corresponding to larger exchange couplings. Moreover, the zero-energy crossings give rise to resonant peaks in the differential conductance with magnitude $4e^2/h$. Finally, we demonstrate that the quantum fluctuations of the dot spin do not alter qualitatively any of the results.
    • Gediminas Kiršanskas, Moshe Goldstein, Karsten Flensberg, Leonid I. Glazman, Jens Paaske
      Journal reference: Phys. Rev. B 92, 235422 (2015) [pdf]
      DOI: 10.1103/PhysRevB.92.235422

    • 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

  • 2014
    • 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

    • Majorana Bound States in Two-Channel Time-Reversal-Symmetric Nanowire Systems - Abstract
      • We consider time-reversal-symmetric two-channel semiconducting quantum wires proximity coupled to an s-wave superconductor. We analyze the requirements for a nontrivial topological phase and find that necessary conditions are 1) the determinant of the pairing matrix in channel space must be negative, 2) inversion symmetry must be broken, and 3) the two channels must have different spin-orbit couplings. The first condition can be implemented in semiconducting nanowire systems where interactions suppress intra-channel pairing, while the inversion symmetry can be broken by tuning the chemical potentials of the channels. For the case of collinear spin-orbit directions, we find a general expression for the topological invariant by block diagonalization into two blocks with chiral symmetry only. By projection to the low-energy sector, we solve for the zero modes explicitly and study the details of the gap closing, which in the general case happens at finite momenta.
    • Erikas Gaidamauskas, Jens Paaske, Karsten Flensberg
      Journal reference: Phys. Rev. Lett. 122, 126402 (2014) [pdf]
      DOI: 10.1103/PhysRevLett.112.126402

  • 2012
    • 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