Center for Quantum Devices > Research > Publications > Jesper Nygård
Publications by Jesper Nygård
 2018

Coupling of shells in a carbon nanotube quantum dot 
Abstract
 We systematically study the coupling of longitudinal modes (shells) in a carbon nanotube quantum dot. Inelastic cotunneling spectroscopy is used to probe the excitation spectrum in parallel, perpendicular and rotating magnetic fields. The data is compared to a theoretical model including coupling between shells, induced by atomically sharp disorder in the nanotube. The calculated excitation spectra show good correspondence with experimental data.
M. C. Hels, T. S. Jespersen, J. Nygård, K. GroveRasmussen 1809.07143v1 [pdf]

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 electronhole and leftright 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 twoimpurity Anderson model.
J. C. Estrada Saldaña, A. Vekris, G. Steffensen, R. Žitko, P. Krogstrup, J. Paaske, K. GroveRasmussen, J. Nygård 1808.05837v1 [pdf]

Observation of 2eperiodic Supercurrents in Nanowire SingleCooperPair
Transistors 
Abstract
 Parity control of superconducting islands hosting Majorana zero modes (MZMs) is required to operate topological qubits made from proximitized semiconductor nanowires. We, therefore, study parity effects in hybrid InAsAl singleCooperpair transistors (SCPTs) as a first step. In particular, we investigate the gatecharge supercurrent modulation and observe a consistent 2$e$periodic pattern indicating a general lack of lowenergy subgap states in these nanowires at zero magnetic field. In a parallel magnetic field, an evenodd pattern develops with a gatecharge spacing that oscillates as a function of field demonstrating that the modulation pattern is sensitive to the presence of a single subgap state. In addition, we find that the parity lifetime of the SCPT decreases exponentially with magnetic field as the subgap state approaches zero energy. Our work highlights the important role that intentional quasiparticle traps and superconducting gap engineering would play in topological qubits that require quenching of the island charge dispersion.
Jasper van Veen, Alex Proutski, Torsten Karzig, Dmitry I. Pikulin, Roman M. Lutchyn, Jesper Nygård, Peter Krogstrup, Attila Geresdi, Leo P. Kouwenhoven, John D. Watson 1805.10266v1 [pdf]

Nearthermal limit gating in heavily doped IIIV semiconductor nanowires using polymer electrolytes 
Abstract
 Doping is a common route to reducing nanowire transistor onresistance but has limits. High doping level gives significant loss in gate performance and ultimately complete gate failure. We show that electrolyte gating remains effective even when the Be doping in our GaAs nanowires is so high that traditional metaloxide gates fail. In this regime we obtain a combination of subthreshold swing and contact resistance that surpasses the best existing ptype nanowire MOSFETs. Our subthreshold swing of 75 mV/dec is within 25% of the roomtemperature thermal limit and comparable with nInP and nGaAs nanowire MOSFETs. Our results open a new path to extending the performance and application of nanowire transistors, and motivate further work on improved solid electrolytes for nanoscale device applications.
A. R. Ullah, D. J. Carrad, P. Krogstrup, J. Nygård, A. P. Micolich Journal reference: Phys. Rev. Materials 2, 025601 (2018) [ 1710.06950v2 ] DOI: 10.1103/PhysRevMaterials.2.025601

Coupling of shells in a carbon nanotube quantum dot 
Abstract
 2017

Engineering hybrid epitaxial InAsSb/Al nanowires for stronger topological protection 
Abstract
 The combination of strong spinorbit coupling, large $g$factors, and the coupling to a superconductor can be used to create a topologically protected state in a semiconductor nanowire. Here we report on growth and characterization of hybrid epitaxial InAsSb/Al nanowires, with varying composition and crystal structure. We find the strongest spinorbit interaction at intermediate compositions in zincblende InAs$_{1x}$Sb$_{x}$ nanowires, exceeding that of both InAs and InSb materials, confirming recent theoretical studies \cite{winkler2016topological}. We show that the epitaxial InAsSb/Al interfaces allows for a hard induced superconducting gap and 2$e$ transport in Coulomb charging experiments, similar to experiments on InAs/Al and InSb/Al materials, and find measurements consistent with topological phase transitions at low magnetic fields due to large effective $g$factors. Finally we present a method to grow pure wurtzite InAsSb nanowires which are predicted to exhibit even stronger spinorbit coupling than the zincblende structure.
Joachim E. Sestoft, Thomas Kanne, Aske Nørskov Gejl, Merlin von Soosten, Jeremy S. Yodh, Daniel Sherman, Brian Tarasinski, Michael Wimmer, Erik Johnson, Mingtang Deng, Jesper Nygård, Thomas Sand Jespersen, Charles M. Marcus, Peter Krogstrup Journal reference: Phys. Rev. Materials 2, 044202 (2018) [ 1711.06864v2 ] DOI: 10.1103/PhysRevMaterials.2.044202

Observation of the 4$π$periodic Josephson effect in InAs nanowires 
Abstract
 Quantum computation by nonAbelian Majorana zero modes (MZMs) offers an approach to achieve fault tolerance by encoding quantum information in the nonlocal charge parity states of semiconductor nanowire networks in the topological superconductor regime. Thus far, experimental studies of MZMs chiefly relied on single electron tunneling measurements which leads to decoherence of the quantum information stored in the MZM. As a next step towards topological quantum computation, charge parity conserving experiments based on the Josephson effect are required, which can also help exclude suggested nontopological origins of the zero bias conductance anomaly. Here we report the direct measurement of the Josephson radiation frequency in InAs nanowires with epitaxial aluminium shells. For the first time, we observe the $4\pi$periodic Josephson effect above a magnetic field of $\approx 200\,$mT, consistent with the estimated and measured topological phase transition of similar devices.

Nonlocality of Majorana modes in hybrid nanowires 
Abstract
 Emergent Majorana bound states (MBSs) in topological superconductors appear capable of providing a naturally faulttolerant basis for quantum computing. Key to topological protection is the separation, or nonlocality, of MBSs, which makes Majorana qubits immune to decoherence by a local disturbance. While a number of experiments have reported signatures of MBSs based on zerobias peaks in tunneling conductance, the nonlocal character of Majorana modes  in contrast to Andreev bound states at zero energy  has not been previously demonstrated. Here, we experimentally demonstrate nonlocality of Majorana modes in epitaxial semiconductorsuperconducting nanowires. This is achieved using recent theory showing that nonlocality can be measured via the interaction of the zeroenergy state in the nanowire with a quantumdot state at one end. By comparing coupling to even versus odd occupied quantum dots states, we measure a high degree of nonlocality, consistent with topological MBSs, as well as the spin canting angles of the Majorana modes.
M. T. Deng, S. Vaitiekénas, E. Prada, P. SanJose, J. Nygård, P. Krogstrup, R. Aguado, C. M. Marcus Journal reference: Phys. Rev. B 98, 085125 (2018) [ 1712.03536v1 ] DOI: 10.1103/PhysRevB.98.085125

Evolution of Nanowire Transmon Qubits and Their Coherence in a Magnetic Field 
Abstract
 We present an experimental study of nanowire transmons at zero and applied inplane magnetic field. With Josephson nonlinearities provided by the nanowires, our qubits operate at higher magnetic fields than standard transmons. Nanowire transmons exhibit coherence up to 70 mT, where the induced superconducting gap in the nanowire closes. We demonstrate that onchip charge noise coupling to the Josephson energy plays a dominant role in the qubit dephasing. This takes the form of stronglycoupled twolevel systems switching on 100 ms timescales and a more weakly coupled background producing $1/f$ noise. Several observations, including the field dependence of qubit energy relaxation and dephasing, are not fully understood, inviting further experimental investigation and theory. Using nanowires with a thinner superconducting shell will enable operation of these circuits up to 0.5 T, a regime relevant for topological quantum computation.
F. Luthi, T. Stavenga, O. W. Enzing, A. Bruno, C. Dickel, N. K. Langford, M. A. Rol, T. S. Jespersen, J. Nygard, P. Krogstrup, L. DiCarlo Journal reference: Phys. Rev. Lett. 120, 100502 (2018) [ 1711.07961v1 ] DOI: 10.1103/PhysRevLett.120.100502

YuShibaRusinov screening of spins in double quantum dots 
Abstract
 A magnetic impurity coupled to a superconductor gives rise to a YuShibaRusinov (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 spin1/2 and spin1 states. Gating the double dot through 9 different charge states, we show that the honeycomb pattern of zerobias conductance peaks, archetypal of double dots coupled to normal leads, is replaced by lines of zeroenergy YSR states. These enclose regions of YSRscreened 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 zerobandwidth approximation, and with numerical renormalization group calculations for the twoorbital Anderson model.
K. GroveRasmussen, G. Steffensen, A. Jellinggaard, M. H. Madsen, R. Žitko, J. Paaske, J. Nygård DOI: 10.1038/s4146701804683x 1711.06081v1 [pdf]

Direct Microwave Measurement of AndreevBoundState Dynamics in a SemiconductorNanowire Josephson Junction 
Abstract
 The modern understanding of the Josephson effect in mesosopic devices derives from the physics of Andreev bound states, fermionic modes that are localized in a superconducting weak link. Recently, Josephson junctions constructed using semiconducting nanowires have led to the realization of superconducting qubits with gatetunable Josephson energies. We have used a microwave circuit QED architecture to detect Andreev bound states in such a gatetunable junction based on an aluminumproximitized InAs nanowire. We demonstrate coherent manipulation of these bound states, and track the boundstate fermion parity in real time. Individual parityswitching events due to nonequilibrium quasiparticles are observed with a characteristic timescale $T_\mathrm{parity} = 160\pm 10~\mathrm{\mu s}$. The $T_\mathrm{parity}$ of a topological nanowire junction sets a lower bound on the bandwidth required for control of Majorana bound states.
M. Hays, G. de Lange, K. Serniak, D. J. van Woerkom, D. Bouman, P. Krogstrup, J. Nygård, A. Geresdi, M. H. Devoret Journal reference: Phys. Rev. Lett. 121, 047001 (2018) [ 1711.01645v1 ] DOI: 10.1103/PhysRevLett.121.047001

Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions 
Abstract
 The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gatetunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates providing a highly scalable and insitu variation of the device properties. In addition, semiconductors with large $g$factor and spinorbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as $\varphi_0$ Josephson junctions and the emergence of Majorana bound states. Here, we report microwave spectroscopy measurements that directly reveal the presence of Andreev bound states (ABS) in ballistic semiconductor channels. We show that the measured ABS spectra are the result of transport channels with gatetunable, high transmission probabilities up to $0.9$, which is required for gatetunable Andreev qubits and beneficial for braiding schemes of Majorana states. For the first time, we detect excitations of a spinsplit pair of ABS and observe symmetrybroken ABS, a direct consequence of the spinorbit coupling in the semiconductor.
David J. van Woerkom, Alex Proutski, Bernard van Heck, Daniël Bouman, Jukka I. Väyrynen, Leonid I. Glazman, Peter Krogstrup, Jesper Nygård, Leo P. Kouwenhoven, Attila Geresdi Journal reference: Nature Physics 13, 876 (2017) [ 1609.00333v2 ] DOI: 10.1038/nphys4150

Effective gfactor in Majorana Wires 
Abstract
 We use the effective gfactor of subgap states, g*, in hybrid InAs nanowires with an epitaxial Al shell to investigate how the superconducting density of states is distributed between the semiconductor core and the metallic shell. We find a steplike reduction of g* and improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and g* exceeding the gfactor of the proximitizing superconductor. Additionally, we observe the closing and reopening of a gap in the subgap spectrum coincident with the appearance of a zerobias conductance peak.
S. Vaitiekėnas, M. T. Deng, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Phys. Rev. Lett. 121, 037703 (2018) [ 1710.04300v1 ] DOI: 10.1103/PhysRevLett.121.037703

Conduction channels of an InAsAl nanowire Josephson weak link 
Abstract
 We present a quantitative characterization of an electrically tunable Josephson junction defined in an InAs nanowire proximitized by an epitaxiallygrown superconducting Al shell. The gatedependence of the number of conduction channels and of the set of transmission coefficients are extracted from the highly nonlinear currentvoltage characteristics. Although the transmissions evolve nonmonotonically, the number of independent channels can be tuned, and configurations with a single quasiballistic channel achieved.
M. F. Goffman, C. Urbina, H. Pothier, J. Nygård, C. M. Marcus, P. Krogstrup Journal reference: New Journal of Physics, Institute of Physics: Open Access Journals, 2017, 19, pp.092002 [ 1706.09150v2 ] DOI: 10.1088/13672630/aa7641

Hybrid Nanowire IontoElectron Transducers for Integrated Bioelectronic Circuitry 
Abstract
 A key task in the emerging field of bioelectronics is the transduction between ionic/protonic and electronic signals at high fidelity. This is a considerable challenge since the two carrier types exhibit intrinsically different physics and are best supported by very different materials types  electronic signals in inorganic semiconductors and ionic/protonic signals in organic or bioorganic polymers, gels or electrolytes. Here we demonstrate a new class of organicinorganic transducing interface featuring semiconducting nanowires electrostatically gated using a solid protontransporting hygroscopic polymer. This model platform allows us to study the basic transducing mechanisms as well as deliver high fidelity signal conversion by tapping into and drawing together the best candidates from traditionally disparate realms of electronic materials research. By combining complementary n and ptype transducers we demonstrate functional logic with significant potential for scaling towards highdensity integrated bioelectronic circuitry.
D. J. Carrad, A. B. Mostert, A. R. Ullah, A. M. Burke, H. J. Joyce, H. H. Tan, C. Jagadish, P. Krogstrup, J. Nygård, P. Meredith, A. P. Micolich Journal reference: Nano Letters 17, 827833 (2017) [ 1705.00611v1 ] DOI: 10.1021/acs.nanolett.6b04075

Towards lowdimensional hole systems in Bedoped GaAs nanowires 
Abstract
 GaAs was central to the development of quantum devices but is rarely used for nanowirebased quantum devices with InAs, InSb and SiGe instead taking the leading role. ptype GaAs nanowires offer a path to studying stronglyconfined 0D and 1D hole systems with strong spinorbit effects, motivating our development of nanowire transistors featuring Bedoped ptype GaAs nanowires, AuBe alloy contacts and patterned local gate electrodes towards making nanowirebased quantum hole devices. We report on nanowire transistors with traditional substrate backgates and EBLdefined metal/oxide topgates produced using GaAs nanowires with three different Bedoping densities and various AuBe contact processing recipes. We show that contact annealing only brings small improvements for the moderatelydoped devices under conditions of lower anneal temperature and short anneal time. We only obtain good transistor performance for moderate doping, with conduction freezing out at low temperature for lowlydoped nanowires and inability to reach a clear offstate under gating for the highlydoped nanowires. Our best devices give onstate conductivity 95 nS, offstate conductivity 2 pS, onoff ratio ~$10^{4}$, and subthreshold slope 50 mV/dec at T = 4 K. Lastly, we made a device featuring a moderatelydoped nanowire with annealed contacts and multiple topgates. Topgate sweeps show a plateau in the subthreshold region that is reproducible in separate cooldowns and indicative of possible conductance quantization highlighting the potential for future quantum device studies in this material system.
A. R. Ullah, J. G. Gluschke, P. Krogstrup, C. B. Sørensen, J. Nygård, A. P. Micolich Journal reference: Nanotechnology 28, 134005 (2017) [ 1704.03957v1 ] DOI: 10.1088/13616528/aa6067

Current–phase relations of fewmode InAs nanowire Josephson junctions 
Abstract
 Gatetunable semiconductor nanowires with superconducting leads have great potential for quantum computation and as model systems for mesoscopic Josephson junctions. The supercurrent, $I$, versus the phase, $\phi$, across the junction is called the currentphase relation (CPR). It can reveal not only the amplitude of the critical current, but also the number of modes and their transmission. We measured the CPR of many individual InAs nanowire Josephson junctions, one junction at a time. Both the amplitude and shape of the CPR varied between junctions, with small critical currents and skewed CPRs indicating fewmode junctions with high transmissions. In a gatetunable junction, we found that the CPR varied with gate voltage: Near the onset of supercurrent, we observed behavior consistent with resonant tunneling through a single, highly transmitting mode. The gate dependence is consistent with modeled subband structure that includes an effective tunneling barrier due to an abrupt change in the Fermi level at the boundary of the gatetuned region. These measurements of skewed, tunable, fewmode CPRs are promising both for applications that require anharmonic junctions and for Majorana readout proposals.
Eric M. Spanton, Mingtang Deng, Saulius Vaitiekėnas, Peter Krogstrup, Jesper Nygård, Charles M. Marcus, Kathryn A. Moler Journal reference: Nature Physics (2017) [ 1701.01188v1 ] DOI: 10.1038/nphys4224

Majorana bound state in a coupled quantumdot hybridnanowire 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 enddot 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, 15571562 (2016) [ 1612.07989v2 ] DOI: 10.1126/science.aaf3961

Engineering hybrid epitaxial InAsSb/Al nanowires for stronger topological protection 
Abstract
 2016

Transport Signatures of Quasiparticle Poisoning in a Majorana Island 
Abstract
 We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normalmetal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 {\mu}s) and sets a bound for a weakly coupled island (> 10 {\mu}s). Fluctuations in the gatevoltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. In energy units, fluctuations are consistent with previous measurements.
S. M. Albrecht, E. B. Hansen, A. P. Higginbotham, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, J. Danon, K. Flensberg, C. M. Marcus Journal reference: Phys. Rev. Lett. 118, 137701 (2017) [ 1612.05748v1 ] DOI: 10.1103/PhysRevLett.118.137701

InAs Nanowire with Epitaxial Aluminum as a SingleElectron Transistor with Fixed Tunnel Barriers 
Abstract
 We report on fabrication of singleelectron transistors using InAs nanowires with epitaxial aluminium with fixed tunnel barriers made of aluminium oxide. The devices exhibit a hard superconducting gap induced by the proximized aluminium cover shell and they behave as metallic singleelectron transistors. In contrast to the typical few channel contacts in semiconducting devices, our approach forms opaque multichannel contacts to a semiconducting wire and thus provides a complementary way to study them. In addition, we confirm that unwanted extra quantum dots can appear at the surface of the nanowire. Their presence is prevented in our devices, and also by inserting a protective layer of GaAs between the InAs and Al, the latter being suitable for standard measurement methods.
M. Taupin, E. Mannila, P. Krogstrup, V. F. Maisi, H. Nguyen, S. M. Albrecht, J. Nygard, C. M. Marcus, J. P. Pekola Journal reference: Phys. Rev. Applied 6, 054017 (2016) [ 1601.01149v4 ] DOI: 10.1103/PhysRevApplied.6.054017

Magnetoresistance engineering and singlet/triplet switching in InAs nanowire quantum dots with ferromagnetic sidegates 
Abstract
 We present magnetoresistance (MR) experiments on an InAs nanowire quantum dot device with two ferromagnetic sidegates (FSGs) in a splitgate geometry. The wire segment can be electrically tuned to a single dot or to a double dot regime using the FSGs and a backgate. In both regimes we find a strong MR and a sharp MR switching of up to 25\% at the field at which the magnetizations of the FSGs are inverted by the external field. The sign and amplitude of the MR and the MR switching can both be tuned electrically by the FSGs. In a double dot regime close to pinchoff we find {\it two} sharp transitions in the conductance, reminiscent of tunneling MR (TMR) between two ferromagnetic contacts, with one transition near zero and one at the FSG switching fields. These surprisingly rich characteristics we explain in several simple resonant tunneling models. For example, the TMRlike MR can be understood as a strayfield controlled transition between singlet and a triplet double dot states. Such local magnetic fields are the key elements in various proposals to engineer novel states of matter and may be used for testing electron spinbased Bell inequalities.
G. Fábián, P. Makk, M. H. Madsen, J. Nygård, C. Schönenberger, A. Baumgartner Journal reference: Phys. Rev. B 94, 195415 (2016) [ 1608.07143v1 ] DOI: 10.1103/PhysRevB.94.195415

Noncollinear SpinOrbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot 
Abstract
 We demonstrate experimentally that noncollinear intrinsic spinorbit magnetic fields can be realized in a curved carbon nanotube twosegment device. Each segment, analyzed in the quantum dot regime, shows near fourfold degenerate shell structure allowing for identification of the spinorbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements.
Morten Canth Hels, Bernd Braunecker, Kasper GroveRasmussen, Jesper Nygård Journal reference: Phys. Rev. Lett. 117, 276802 (2016) [ 1606.01065v1 ] DOI: 10.1103/PhysRevLett.117.276802

Normal, superconducting and topological regimes of hybrid double quantum dots 
Abstract
 Epitaxial semiconductorsuperconductor hybrid materials are an excellent basis for studying mesoscopic and topological superconductivity, as the semiconductor inherits a hard superconducting gap while retaining tunable carrier density. Here, we investigate doublequantumdot devices made from InAs nanowires with a patterned epitaxial Al twofacet shell that proximitizes two gatedefined segments along the nanowire. We follow the evolution of mesoscopic superconductivity and charging energy in this system as a function of magnetic field and voltagetuned barriers. Interdot coupling is varied from strong to weak using side gates, and the ground state is varied between normal, superconducting, and topological regimes by applying a magnetic field. We identify the topological transition by tracking the spacing between successive cotunneling peaks as a function of axial magnetic field and show that the individual dots host weakly hybridized Majorana modes.
D. Sherman, J. S. Yodh, S. M. Albrecht, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Nature Nanotechnology 12, 212 (2017) [ 1605.01865v1 ] DOI: 10.1038/nnano.2016.227

Exponential protection of zero modes in Majorana islands 
Abstract
 Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of faulttolerant quantum computers [1]. They are expected to exhibit nonAbelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, and the pinning is predicted to be exponential as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in proximitized nanowires and atomic chains, with small modesplitting potentially explained by hybridization of Majoranas. Here, we use Coulombblockade spectroscopy in an InAs nanowire segment with epitaxial aluminum, which forms a proximityinduced superconducting Coulomb island (a Majorana island) that is isolated from normalmetal leads by tunnel barriers, to measure the splitting of nearzeroenergy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometers, subgap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half micrometer of increased wire length. For devices longer than about one micrometer, transport in strong magnetic fields occurs through a zeroenergy state that is energetically isolated from a continuum, yielding uniformly spaced Coulombblockade conductance peaks, consistent with teleportation via Majorana modes. Our results help explain the trivialtotopological transition in finite systems and to quantify the scaling of topological protection with endmode separation.
S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Nature 531, 206 (2016) [pdf] DOI: 10.1038/nature17162

Raman spectroscopy and electrical properties of InAs nanowires with local oxidation enabled by substrate microtrenches and laser irradiation 
Abstract
 The thermal gradient along indiumarsenide nanowires was engineered by a combination of fabricated micro trenches in the supporting substrate and focused laser irradiation. This allowed local control of thermally activated oxidation reactions of the nanowire on the scale of the diffraction limit. The locality of the oxidation was detected by microRaman mapping, and the results were found consistent with numerical simulations of the temperature profile. Applying the technique to nanowires in electrical devices the locally oxidized nanowires remained conducting with a lower conductance as expected for an effectively thinner conducting core.
R. Tanta, M. H. Madsen, Z. Liao, P. Krogstrup, T. Vosch, J. Nygard, T. S. Jespersen Journal reference: Appl. Phys. Lett. 107, 243101 (2015) [ 1601.06583v1 ] DOI: 10.1063/1.4937442

Transport Signatures of Quasiparticle Poisoning in a Majorana Island 
Abstract
 2015

Gigahertz Quantized Charge Pumping in BottomGateDefined InAs Nanowire Quantum Dots 
Abstract
 Semiconducting nanowires (NWs) are a versatile, highly tunable material platform at the heart of many new developments in nanoscale and quantum physics. Here, we demonstrate charge pumping, i.e., the controlled transport of individual electrons through an InAs NW quantum dot (QD) device at frequencies up to $1.3\,$GHz. The QD is induced electrostatically in the NW by a series of local bottom gates in a state of the art device geometry. A periodic modulation of a single gate is enough to obtain a dc current proportional to the frequency of the modulation. The dc bias, the modulation amplitude and the gate voltages on the local gates can be used to control the number of charges conveyed per cycle. Charge pumping in InAs NWs is relevant not only in metrology as a current standard, but also opens up the opportunity to investigate a variety of exotic states of matter, e.g. Majorana modes, by single electron spectroscopy and correlation experiments.
S. d'Hollosy, M. Jung, A. Baumgartner, V. A. Guzenko, M. H. Madsen, J. Nygård, C. Schönenberger Journal reference: Nano Lett. 15, 4585 (2015) [pdf] DOI: 10.1021/acs.nanolett.5b01190

Magnetic Field Tuning and Quantum Interference in a Cooper Pair Splitter 
Abstract
 Cooper pair splitting (CPS) is a process in which the electrons of naturally occurring spinsinglet pairs in a superconductor are spatially separated using two quantum dots. Here we investigate the evolution of the conductance correlations in an InAs CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fanotype resonance with increasing field. These experiments can be understood in a simple three  site model, which shows that the nonlocal CPS leads to symmetric line shapes, while the local transport processes can exhibit an asymmetric shape due to quantum interference. These findings demonstrate that the electrons from a Cooper pair splitter can propagate coherently after their emission from the superconductor and how a magnetic field can be used to optimize the performance of a CPS device. In addition, the model calculations suggest that the estimate of the CPS efficiency in the experiments is a lower bound for the actual efficiency.
G. Fülöp, F. Domínguez, S. d'Hollosy, A. Baumgartner, P. Makk, M. H. Madsen, V. A. Guzenko, J. Nygård, C. Schönenberger, A. Levy Yeyati, S. Csonka Journal reference: Phys. Rev. Lett. 115, 227003 (2015) [pdf] DOI: 10.1103/PhysRevLett.115.227003

Quantum transport in carbon nanotubes 
Abstract
 Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spinorbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electronelectron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the wellunderstood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.
E. A. Laird, F. Kuemmeth, G. Steele, K. GroveRasmussen, J. Nygård, K. Flensberg, L. P. Kouwenhoven Journal reference: Rev. Mod. Phys. 87, 703 (2015) [pdf] DOI: 10.1103/RevModPhys.87.703

SemiconductorNanowireBased Superconducting Qubit 
Abstract
 We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmonlike device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an onchip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (0.8 {\mu}s) and dephasing times (1 {\mu}s), exceeding gate operation times by two orders of magnitude, in these firstgeneration devices. Because qubit control relies on voltages rather than fluxes, dissipation in resistive control lines is reduced, screening reduces crosstalk, and the absence of flux control allows operation in a magnetic field, relevant for topological quantum information.
T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, J. Nygard, C. M. Marcus Journal reference: Phys. Rev. Lett. 115, 127001 (2015) [pdf] DOI: 10.1103/PhysRevLett.115.127001

Hard gap in epitaxial semiconductor–superconductor nanowires 
Abstract
 Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunneling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunneling conductance below the superconducting gap, suggesting a continuum of subgap statesa situation that nullifies topological protection. Here, we report a hard superconducting gap induced by proximity effect in a semiconductor, using epitaxial AlInAs superconductorsemiconductor nanowires. The hard gap, along with favorable material properties and gatetunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.
W. Chang, S. M. Albrecht, T. S. Jespersen, F. Kuemmeth, P. Krogstrup, J. Nygård, C. M. Marcus Journal reference: Nature Nanotechnology 10, 232 (2015) [pdf] DOI: 10.1038/nnano.2014.306

Parity lifetime of bound states in a proximitized semiconductor nanowire 
Abstract
 Quasiparticle excitations can compromise the performance of superconducting devices, causing high frequency dissipation, decoherence in Josephson qubits, and braiding errors in proposed Majoranabased topological quantum computers. Quasiparticle dynamics have been studied in detail in metallic superconductors but remain relatively unexplored in semiconductorsuperconductor structures, which are now being intensely pursued in the context of topological superconductivity. To this end, we introduce a new physical system comprised of a gateconfined semiconductor nanowire with an epitaxially grown superconductor layer, yielding an isolated, proximitized nanowire segment. We identify Andreevlike bound states in the semiconductor via bias spectroscopy, determine the characteristic temperatures and magnetic fields for quasiparticle excitations, and extract a parity lifetime (poisoning time) of the bound state in the semiconductor exceeding 10 ms.
A. P. Higginbotham, S. M. Albrecht, G. Kirsanskas, W. Chang, F. Kuemmeth, P. Krogstrup, T. S. Jespersen, J. Nygard, K. Flensberg, C. M. Marcus Journal reference: Nature Physics 11, 1017 (2015) [pdf] DOI: 10.1038/nphys3461

Gigahertz Quantized Charge Pumping in BottomGateDefined InAs Nanowire Quantum Dots 
Abstract
 2014

Epitaxy of semiconductor–superconductor nanowires 
Abstract
 Controlling the properties of semiconductor/metal interfaces is a powerful method for designing functionality and improving the performance of electrical devices. Recently semiconductor/superconductor hybrids have appeared as an important example where the atomic scale uniformity of the interface plays a key role for the quality of the induced superconducting gap. Here we present epitaxial growth of semiconductormetal coreshell nanowires by molecular beam epitaxy, a method that provides a conceptually new route to controlled electrical contacting of nanostructures and for designing devices for specialized applications such as topological and gatecontrolled superconducting electronics. Our materials of choice, InAs/Al, are grown with epitaxially matched single plane interfaces, and alternative semiconductor/metal combinations allowing epitaxial interface matching in nanowires are discussed. We formulate the grain growth kinetics of the metal phase in general terms of continuum parameters and bicrystal symmetries. The method realizes the ultimate limit of uniform interfaces and appears to solve the softgap problem in superconducting hybrid structures.
P. Krogstrup, N. L. B. Ziino, W. Chang, S. M. Albrecht, M. H. Madsen, E. Johnson, J. Nygård, C. M. Marcus, T. S. Jespersen Journal reference: Nature Materials 14, 400 (2015) [pdf] DOI: 10.1038/nmat4176

Local electrical tuning of the nonlocal signals in a Cooper pair splitter 
Abstract
 A Cooper pair splitter consists of a central superconducting contact, S, from which electrons are injected into two parallel, spatially separated quantum dots (QDs). This geometry and electron interactions can lead to correlated electrical currents due to the spatial separation of spinsinglet Cooper pairs from S. We present experiments on such a device with a series of bottom gates, which allows for spatially resolved tuning of the tunnel couplings between the QDs and the electrical contacts and between the QDs. Our main findings are gateinduced transitions between positive conductance correlation in the QDs due to Cooper pair splitting and negative correlations due to QD dynamics. Using a semiclassical rate equation model we show that the experimental findings are consistent with insitu electrical tuning of the local and nonlocal quantum transport processes. In particular, we illustrate how the competition between Cooper pair splitting and local processes can be optimized in such hybrid nanostructures.
G. Fülöp, S. d'Hollosy, A. Baumgartner, P. Makk, V. A. Guzenko, M. H. Madsen, J. Nygård, C. Schönenberger, S. Csonka Journal reference: Phys. Rev. B 90, 235412 (2014) [pdf] DOI: 10.1103/PhysRevB.90.235412

Epitaxy of semiconductor–superconductor nanowires 
Abstract
 2013

Epitaxial aluminum contacts to InAs nanowires 
Abstract
 We report a method for making epitaxial superconducting contacts to semiconducting nanowires. The temperature and gate characteristics demonstrate barrierfree electrical contact, and the properties in the superconducting state are investigated at low temperature. Halfcovering aluminum contacts are realized without the need of lithography and we demonstrate how to controllably insert highband gap layers in the interface region. These developments are relevant to hybrid superconductornanowire devices that support Majorana zero energy states.
N. L. B. Ziino, P. Krogstrup, M. H. Madsen, E. Johnson, J. B. Wagner, C. M. Marcus, J. Nygård, T. S. Jespersen 1309.4569v1 [pdf]

AIP Conference Proceedingsgfactor anisotropy in nanowirebased InAs quantum dots 
Abstract
 The determination and control of the electron $g$factor in semiconductor quantum dots (QDs) are fundamental prerequisites in modern concepts of spintronics and spinbased quantum computation. We study the dependence of the $g$factor on the orientation of an external magnetic field in quantum dots (QDs) formed between two metallic contacts on stacking fault free InAs nanowires. We extract the $g$factor from the splitting of Kondo resonances and find that it varies continuously in the range between $g^* = 5$ and 15.
Samuel d'Hollosy, Gábor Fábián, Andreas Baumgartner, Jesper Nygård, Christian Schönenberger Journal reference: AIP Conf. Proc. 1566, 359 (2013) [ 1309.0726v1 ] DOI: 10.1063/1.4848434

Advances in the theory of III–V nanowire growth dynamics 
Abstract
 Nanowire (NW) crystal growth via the vapour_liquid_solid mechanism is a complex dynamic process involving interactions between many atoms of various thermodynamic states. With increasing speed over the last few decades many works have reported on various aspects of the growth mechanisms, both experimentally and theoretically. We will here propose a general continuum formalism for growth kinetics based on thermodynamic parameters and transition state kinetics. We use the formalism together with key elements of recent research to present a more overall treatment of III_V NW growth, which can serve as a basis to model and understand the dynamical mechanisms in terms of the basic control parameters, temperature and pressures/beam fluxes. Selfcatalysed GaAs NW growth on Si substrates by molecular beam epitaxy is used as a model system.
Peter Krogstrup, Henrik I. Jørgensen, Erik Johnson, Morten Hannibal Madsen, Claus B. Sørensen, Anna Fontcuberta i Morral, Martin Aagesen, Jesper Nygård, Frank Glas Journal reference: J. Phys. D: Appl. Phys. 46 (2013) 313001 [pdf] DOI: 10.1088/00223727/46/31/313001

A highmobility twodimensional electron gas at the spinel/perovskite interface of γAl2O3/SrTiO3 
Abstract
 The discovery of twodimensional electron gases (2DEGs) at the heterointerface between two insulating perovskitetype oxides, such as LaAlO3 and SrTiO3, provides opportunities for a new generation of alloxide electronic and photonic devices. However, significant improvement of the interfacial electron mobility beyond the current value of approximately 1,000 cm2V1s1 (at low temperatures), remains a key challenge for fundamental as well as applied research of complex oxides. Here, we present a new type of 2DEG created at the heterointerface between SrTiO3 and a spinel {\gamma}Al2O3 epitaxial film with excellent quality and compatible oxygen ions sublattices. This spinel/perovskite oxide heterointerface exhibits electron mobilities more than one order of magnitude higher than those of perovskite/perovskite oxide interfaces, and demonstrates unambiguous twodimensional conduction character as revealed by the observation of quantum magnetoresistance oscillations. Furthermore, we find that the spinel/perovskite 2DEG results from interfacestabilized oxygen vacancies and is confined within a layer of 0.9 nm in proximity to the heterointerface. Our findings pave the way for studies of mesoscopic physics with complex oxides and design of highmobility alloxide electronic devices.
Y. Z. Chen, N. Bovet, F. Trier, D. V. Christensen, F. M. Qu, N. H. Andersen, T. Kasama, W. Zhang, R. Giraud, J. Dufouleur, T. S. Jespersen, J. R. Sun, A. Smith, J. Nygård, L. Lu, B. Büchner, B. G. Shen, S. Linderoth, N. Pryds Journal reference: Nature Communications, Nat Commun. 2013;4:1371 [pdf] DOI: 10.1038/ncomms2394

Singlenanowire solar cells beyond the Shockley–Queisser limit 
Abstract
 Light management is of great importance to photovoltaic cells, as it determines the fraction of incident light entering the device. An optimal pnjunction combined with an optimal light absorption can lead to a solar cell efficiency above the ShockleyQueisser limit. Here, we show how this is possible by studying photocurrent generation for a single coreshell pin junction GaAs nanowire solar cell grown on a silicon substrate. At one sun illumination a short circuit current of 180 mA/cm^2 is obtained, which is more than one order of magnitude higher than what would be predicted from LambertBeer law. The enhanced light absorption is shown to be due to a light concentrating property of the standing nanowire as shown by photocurrent maps of the device. The results imply new limits for the maximum efficiency obtainable with IIIV based nanowire solar cells under one sun illumination.
Peter Krogstrup, Henrik Ingerslev Jørgensen, Martin Heiss, Olivier Demichel, Jeppe V. Holm, Martin Aagesen, Jesper Nygard, Anna Fontcuberta i Morral Journal reference: Nature Photonics 7, 306310 (2013) [pdf] DOI: 10.1038/nphoton.2013.32

Epitaxial aluminum contacts to InAs nanowires 
Abstract
 2012

Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction 
Abstract
 The spectrum of a segment of InAs nanowire, confined between two superconducting leads, was measured as function of gate voltage and superconducting phase difference using a third normalmetal tunnel probe. Subgap resonances for odd electron occupancyinterpreted as bound states involving a confined electron and a quasiparticle from the superconducting leads, reminiscent of YuShibaRusinov statesevolve into Kondorelated resonances at higher magnetic fields. An additional zero bias peak of unknown origin is observed to coexist with the quasiparticle bound states.
W. Chang, V. E. Manucharyan, T. S. Jespersen, J. Nygard, C. M. Marcus Journal reference: Phys. Rev. Lett. 110, 217005 (2013) [pdf] DOI: 10.1103/PhysRevLett.110.217005

Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction 
Abstract
 2011

FiniteBias Cooper Pair Splitting 
Abstract
 In a device with a superconductor coupled to two parallel quantum dots (QDs) the electrical tunability of the QD levels can be used to exploit nonclassical current correlations due to the splitting of Cooper pairs. We experimentally investigate the effect of a finite potential difference across one quantum dot on the conductance through the other completely grounded QD in a Cooper pair splitter fabricated on an InAs nanowire. We demonstrate that the electrical transport through the device can be tuned by electrical means to be dominated either by Cooper pair splitting (CPS), or by elastic cotunneling (EC). The basic experimental findings can be understood by considering the energy dependent density of states in a QD. The reported experiments add biasdependent spectroscopy to the investigative tools necessary to develop CPSbased sources of entangled electrons in solidstate devices.
L. Hofstetter, S. Csonka, A. Baumgartner, Fülöp, S. d'Hollosy, J. Nygård, C. Schönenberger Journal reference: Phys. Rev. Lett. 107, 136801 (2011) [pdf] DOI: 10.1103/PhysRevLett.107.136801

FiniteBias Cooper Pair Splitting 
Abstract
 2010

Ferromagnetic Proximity Effect in a Ferromagnet–QuantumDot–Superconductor Device 
Abstract
 Ferromagnetic proximity effect is studied in InAs nanowire (NW) based quantum dots (QD) strongly coupled to a ferromagnetic (F) and a superconducting (S) lead. The influence of the F lead is detected through the splitting of the spin1/2 Kondo resonance. We show that the F lead induces a local exchange field on the QD, which has varying amplitude and a sign depending on the charge states. The interplay of the F and S correlations generates an exchange field related supgap feature. This novel minigap allows now the visualization of the exchange field also in even charge states
L. Hofstetter, S. Csonka, A. Geresdi, M. Aagesen, J. Nygard, C. Schonenberger Journal reference: Phys. Rev. Lett. 104, 246804 (2010) [pdf] DOI: 10.1103/PhysRevLett.104.246804

Nanoelectromechanical coupling in fullerene peapods probed by resonant electrical transport experiments 
Abstract
 Fullerene peapods, that is carbon nanotubes encapsulating fullerene molecules, can offer enhanced functionality with respect to empty nanotubes. However, the present incomplete understanding of how a nanotube is affected by entrapped fullerenes is an obstacle for peapods to reach their full potential in nanoscale electronic applications. Here, we investigate the effect of C60 fullerenes on electron transport via peapod quantum dots. Compared to empty nanotubes, we find an abnormal temperature dependence of Coulomb blockade oscillations, indicating the presence of a nanoelectromechanical coupling between electronic states of the nanotube and mechanical vibrations of the fullerenes. This provides a method to detect the C60 presence and to probe the interplay between electrical and mechanical excitations in peapods, which thus emerge as a new class of nanoelectromechanical systems.
Pawel Utko, Raffaello Ferone, Ilya V. Krive, Robert I. Shekhter, Mats Jonson, Marc Monthioux, Laure Noé, Jesper Nygård Journal reference: Nat. Commun. 1, 37 (2010) [pdf] DOI: 10.1038/ncomms1034

Gatedependent spinorbit coupling in multielectron carbon nanotubes 
Abstract
 Understanding how the orbital motion of electrons is coupled to the spin degree of freedom in nanoscale systems is central for applications in spinbased electronics and quantum computation. We demonstrate this coupling of spin and orbit in a carbon nanotube quantum dot in the general multielectron regime in presence of finite disorder. Further, we find a strong systematic dependence of the spinorbit coupling on the electron occupation of the quantum dot. This dependence, which even includes a sign change is not demonstrated in any other system and follows from the curvatureinduced spinorbit split Diracspectrum of the underlying graphene lattice. Our findings unambiguously show that the spinorbit coupling is a general property of nanotube quantum dots which provide a unique platform for the study of spinorbit effects and their applications.
Thomas Sand Jespersen, Kasper GroveRasmussen, Jens Paaske, Koji Muraki, Toshimasa Fujisawa, Jesper Nygård, Karsten Flensberg 1008.1600v2 [pdf]

Transport via coupled states in a C60 peapod quantum dot 
Abstract
 We have measured systematic repetitions of avoided crossings in low temperature threeterminal 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 welldefined 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]

Ferromagnetic Proximity Effect in a Ferromagnet–QuantumDot–Superconductor Device 
Abstract
 2009

Mesoscopic conductance fluctuations in InAs nanowirebased SNS junctions 
Abstract
 We report a systematic experimental study of mesoscopic conductance fluctuations in superconductor/normal/superconductor (SNS) devices Nb/InAsnanowire/Nb. These fluctuations far exceed their value in the normal state and strongly depend on temperature even in the lowtemperature regime. This dependence is attributed to high sensitivity of perfectly conducting channels to dephasing and the SNS fluctuations thus provide a sensitive probe of dephasing in a regime where normal transport fails to detect it. Further, the conductance fluctuations are strongly nonlinear in bias voltage and reveal subgap structure. The experimental findings are qualitatively explained in terms of multiple Andreev reflections in chaotic quantum dots with imperfect contacts.
T. S. Jespersen, M. L. Polianski, C. B. Soerensen, K. Flensberg, J. Nygaard Journal reference: New J. Phys. 11, 113025 (2009) [pdf] DOI: 10.1088/13672630/11/11/113025

Superconductivityenhanced bias spectroscopy in carbon nanotube quantum dots 
Abstract
 We study lowtemperature transport through carbon nanotube quantum dots in the Coulomb blockade regime coupled to niobiumbased superconducting leads. We observe pronounced conductance peaks at finite sourcedrain bias, which we ascribe to elastic and inelastic cotunneling processes enhanced by the coherence peaks in the density of states of the superconducting leads. The inelastic cotunneling lines display a marked dependence on the applied gate voltage which we relate to different tunnelingrenormalizations of the two subbands in the nanotube. Finally, we discuss the origin of an especially pronounced subgap structure observed in every fourth Coulomb diamond.
K. GroveRasmussen, H. I. Jørgensen, B. M. Andersen, J. Paaske, T. S. Jespersen, J. Nygård, K. Flensberg, P. E. Lindelof Journal reference: Phys. Rev. B 79, 134518 (2009) [pdf] DOI: 10.1103/PhysRevB.79.134518

Nonequilibrium cotunneling through a threelevel quantum dot 
Abstract
 We calculate the nonlinear cotunneling conductance through a quantum dot with 3 electrons occupying the three highest lying energy levels. Starting from a 3orbital Anderson model, we apply a generalized SchriefferWolff transformation to derive an effective Kondo model for the system. Within this model we calculate the nonequilibrium occupation numbers and the corresponding cotunneling current to leading order in the exchange couplings. We identify the inelastic cotunneling thresholds and their splittings with applied magnetic field, and make a qualitative comparison to recent experimental data on carbon nanotube and InAs quantumwire quantum dots. Further predictions of the model like cascade resonances and a magneticfield dependence of the orbital level splitting are not yet observed but within reach of recent experimental work on carbon nanotube and InAs nanowire quantum dots.
S. Schmaus, V. Koerting, J. Paaske, T. S. Jespersen, J. Nygård, P. Wölfle Journal reference: Phys. Rev. B 79, 045105 (2009) [pdf] DOI: 10.1103/PhysRevB.79.045105

Mesoscopic conductance fluctuations in InAs nanowirebased SNS junctions 
Abstract
 2008

Giant fluctuations and gate control of the gfactor in InAs Nanowire
Quantum Dots 
Abstract
 We study the gfactor of discrete electron states in InAs nanowire based quantum dots. The g values are determined from the magnetic field splitting of the zero bias anomaly due to the spin 1/2Kondo effect. Unlike to previous studies based on 2DEG quantum dots, the gfactors of neighboring electron states show a surprisingly large fluctuation: g can scatter between 2 and 18. Furthermore electric gate tunability of the gfactor is demonstrated.
S. Csonka, L. Hofstetter, F. Freitag, S. Oberholzer, T. S. Jespersen, M. Aagesen, J. Nygard, C. Schonenberger DOI: 10.1021/nl802418w 0808.1492v2 [pdf]

The influence of electromechanical effects on resonant electron tunneling through small carbon nanopeapods 
Abstract
 The influence of a fullerene molecule trapped inside a singlewall carbon nanotube on resonant electron transport at low temperatures and strong polaronic coupling is theoretically discussed. Strong peak to peak fluctuations and anomalous temperature behavior of conductance amplitudes are predicted and investigated. The influence of the chiral properties of carbon nanotubes on transport is also studied.
I. V. Krive, R. Ferone, R. I. Shekhter, M. Jonson, P. Utko, J. Nygård Journal reference: New J. Phys. 10 (2008) 043043 [ condmat/0702153v2 ] DOI: 10.1088/13672630/10/4/043043

Giant fluctuations and gate control of the gfactor in InAs Nanowire
Quantum Dots 
Abstract
 2007

KondoEnhanced Andreev Tunneling in InAs Nanowire Quantum Dots 
Abstract
 We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with subgappeaks at $V_{sd}=\Delta/e$ markedly stronger(weaker) than the quasiparticle tunneling peaks at $V_{sd}=2\Delta/e$ for odd(even) occupation. We attribute the enhanced $\Delta$peak to an interplay between Kondocorrelations and Andreev tunneling in dots with an odd number of spins, and substantiate this interpretation by a poor man's scaling analysis.
T. SandJespersen, J. Paaske, B. M. Andersen, K. GroveRasmussen, H. I. Jørgensen, M. Aagesen, C. Sørensen, P. E. Lindelof, K. Flensberg, J. Nygård Journal reference: Phys. Rev. Lett. 99, 126603 (2007) [ condmat/0703264v1 ] DOI: 10.1103/PhysRevLett.99.126603

KondoEnhanced Andreev Tunneling in InAs Nanowire Quantum Dots 
Abstract
 2006

Kondo physics in tunable semiconductor nanowire quantum dots 
Abstract
 We have observed the Kondo effect in strongly coupled semiconducting nanowire quantum dots. The devices are made from indium arsenide nanowires, grown by molecular beam epitaxy, and contacted by titanium leads. The device transparency can be tuned by changing the potential on a gate electrode, and for increasing transparencies the effects dominating the transport changes from Coulomb Blockade to Universal Conductance Fluctuations with Kondo physics appearing in the intermediate region.
T. S. Jespersen, M. Aagesen, C. Soerensen, P. E. Lindelof, J. Nygaard DOI: 10.1103/PhysRevB.74.233304 condmat/0608478v1 [pdf]

Nonequilibrium singlet–triplet Kondo effect in carbon nanotubes 
Abstract
 The Kondoeffect is a manybody phenomenon arising due to conduction electrons scattering off a localized spin. Coherent spinflip scattering off such a quantum impurity correlates the conduction electrons and at low temperature this leads to a zerobias conductance anomaly. This has become a common signature in biasspectroscopy of singleelectron transistors, observed in GaAs quantum dots as well as in various singlemolecule transistors. While the zerobias Kondo effect is well established it remains uncertain to what extent Kondo correlations persist in nonequilibrium situations where inelastic processes induce decoherence. Here we report on a pronounced conductance peak observed at finite biasvoltage in a carbon nanotube quantum dot in the spin singlet ground state. We explain this finitebias conductance anomaly by a nonequilibrium Kondoeffect involving excitations into a spin triplet state. Excellent agreement between calculated and measured nonlinear conductance is obtained, thus strongly supporting the correlated nature of this nonequilibrium resonance.
J. Paaske, A. Rosch, P. Woelfle, N. Mason, C. M. Marcus, J. Nygard Journal reference: Nature Physics, vol. 2, p.460  464 (2006) [ condmat/0602581v1 ] DOI: 10.1038/nphys340

Kondo physics in tunable semiconductor nanowire quantum dots 
Abstract
 2004

Zerofield splitting of Kondo resonances in a carbon nanotube quantum
dot 
Abstract
 We present lowtemperature electron transport measurements on a singlewall carbon nanotube quantum dot exhibiting Kondo resonances at low temperature. Contrary to the usual behavior for the spin1/2 Kondo effect we find that the temperature dependence of the zero bias conductance is nonmonotonic. In nonlinear transport measurements lowenergy splittings of the Kondo resonances are observed at zero magnetic field. We suggest that these anomalies reflect interactions between the nanotube and a magnetic (catalyst) particle. The nanotube device may effectively act as a ferromagnetically contacted Kondo dot.
J. Nygard, W. F. Koehl, N. Mason, L. DiCarlo, C. M. Marcus condmat/0410467v2 [pdf]

Zerofield splitting of Kondo resonances in a carbon nanotube quantum
dot 
Abstract
 2001

Shell filling in closed singlewall carbon nanotube quantum dots 
Abstract
 We observe twofold shell filling in the spectra of closed onedimensional quantum dots formed in singlewall carbon nanotubes. Its signatures include a bimodal distribution of addition energies, correlations in the excitation spectra for different electron number, and alternation of the spins of the added electrons. This provides a contrast with quantum dots in higher dimensions, where such spin pairing is absent. We also see indications of an additional fourfold periodicity indicative of KK' subband shells. Our results suggest that the absence of shell filling in most isolated nanotube dots results from disorder or nonuniformity.
David H. Cobden, Jesper Nygard DOI: 10.1103/PhysRevLett.89.046803 condmat/0112331v1 [pdf]

Quantum dots in suspended singlewall carbon nanotubes 
Abstract
 We present a simple technique which uses a selfaligned oxide etch to suspend individual singlewall carbon nanotubes between metallic electrodes. This enables one to compare the properties of a particular nanotube before and after suspension, as well as to study transport in suspended tubes. As an example of the utility of the technique, we study quantum dots in suspended tubes, finding that their capacitances are reduced owing to the removal of the dielectric substrate.
Jesper Nygard, David H. Cobden Journal reference: Applied Physics Letters 79 25 4216 (2001) [ condmat/0108020v1 ] DOI: 10.1063/1.1428117#

Transport phenomena in nanotube quantum dots from strong to weak
confinement 
Abstract
 We report lowtemperature transport experiments on singlewall nanotubes with metallic leads of varying contact quality, ranging from weak tunneling to almost perfect transmission. In the weak tunneling regime, where Coulomb blockade dominates, the nanotubes act as onedimensional quantum dots. For stronger coupling to the leads the conductance can be strongly enhanced by inelastic cotunneling and the Kondo effect. For open contacts Coulomb blockade is completely suppressed, and the lowtemperature conductance remains generally high, although we often see distinct dips in the conductance versus gate voltage which may result from resonant backscattering.
Jesper Nygard, David H. Cobden condmat/0105289v1 [pdf]

Shell filling in closed singlewall carbon nanotube quantum dots 
Abstract
 2000

Kondo physics in carbon nanotubes 
Abstract
 The connection of electrical leads to wirelike molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as onedimensional quantum dots, Luttingerliquids, proximityinduced superconductors and ballistic and diffusive onedimensional metals. Here we report that electricallycontacted singlewall nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced lowtemperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far higher tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondolike effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are onedimensional quantum dots with threedimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron number (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.
Jesper Nygard, David Henry Cobden, Poul Erik Lindelof Journal reference: Nature 408, 3426 (2000) [ condmat/0011310v1 ] DOI: 10.1038/35042545

Bias and temperature dependence of the 0.7 conductance anomaly in quantum point contacts 
Abstract
 The 0.7 (2e^2/h) conductance anomaly is studied in strongly confined, etched GaAs/GaAlAs quantum point contacts, by measuring the differential conductance as a function of sourcedrain and gate bias as well as a function of temperature. We investigate in detail how, for a given gate voltage, the differential conductance depends on the finite bias voltage and find a socalled selfgating effect, which we correct for. The 0.7 anomaly at zero bias is found to evolve smoothly into a conductance plateau at 0.85 (2e^2/h) at finite bias. Varying the gate voltage the transition between the 1.0 and the 0.85 (2e^2/h) plateaus occurs for definite bias voltages, which defines a gate voltage dependent energy difference $\Delta$. This energy difference is compared with the activation temperature T_a extracted from the experimentally observed activated behavior of the 0.7 anomaly at low bias. We find \Delta = k_B T_a which lends support to the idea that the conductance anomaly is due to transmission through two conduction channels, of which the one with its subband edge \Delta below the chemical potential becomes thermally depopulated as the temperature is increased.
A. Kristensen, H. Bruus, A. E. Hansen, J. B. Jensen, P. E. Lindelof, C. J. Marckmann, J. Nygard, C. B. Sorensen, F. Beuscher, A. Forchel, M. Michel Journal reference: Phys. Rev. B 62, 10950  10957 (2000) [ condmat/0005082v1 ] DOI: 10.1103/PhysRevB.62.10950

Kondo physics in carbon nanotubes 
Abstract
 1999

Onedimensional transport in bundles of singlewalled carbon nanotubes 
Abstract
 We report measurements of the temperature and gate voltage dependence for individual bundles (ropes) of singlewalled nanotubes. When the conductance is less than about e^2/h at room temperature, it is found to decrease as an approximate power law of temperature down to the region where Coulomb blockade sets in. The powerlaw exponents are consistent with those expected for electron tunneling into a Luttinger liquid. When the conductance is greater than e^2/h at room temperature, it changes much more slowly at high temperatures, but eventually develops very large fluctuations as a function of gate voltage when sufficiently cold. We discuss the interpretation of these results in terms of transport through a Luttinger liquid.
David H. Cobden, Jesper Nygard, Marc Bockrath, Paul L. McEuen DOI: 10.1063/1.59816 condmat/9904179v1 [pdf]

Onedimensional transport in bundles of singlewalled carbon nanotubes 
Abstract
 1998

Activated Behavior of the 0.7 2(e^2)/h Conductance Anomaly in Quantum
Point Contacts 
Abstract
 The 0.7 conductance anomaly in the quantized conductance of trench etched GaAs quantum point contacts is studied experimentally. The temperature dependence of the anomaly measured with vanishing sourcedrain bias reveals the same activated behavior as reported earlier for topgated structures. Our main result is that the zero bias, high temperature 0.7 anomaly found in activation measurements and the finite bias, low temperature 0.9 anomaly found in transport spectroscopy have the same origin: a density dependent excitation gap.
A. Kristensen, H. Bruus, A. Forchel, J. B. Jensen, P. E. Lindelof, M. Michel, J. Nygard, C. B. Sorensen condmat/9808007v2 [pdf]

Temperature dependence of the “0.7” 2e2/h quasiplateau in strongly confined quantum point contacts 
Abstract
 We present new results of the ``0.7'' 2(e^2)/h structure or quasi plateau in some of the most strongly confined point contacts so far reported. This strong confinement is obtained by a combination of shallow etching and metal gate deposition on modulation doped GaAs/GaAlAs heterostructures. The resulting subband separations are up to 20 meV, and as a consequence the quantized conductance can be followed at temperatures up to 30 K, an order of magnitude higher than in conventional split gate devices. We observe pronounced quasi plateaus at several of the lowest conductance steps all the way from their formation around 1 K to 30 K, where the entire conductance quantization is smeared out thermally. We study the deviation of the conductance from ideal integer quantization as a function of temperature, and we find an activated behavior, exp(T_a/T), with a density dependent activation temperature T_a of the order of 2 K. We analyze our results in terms of a simple theoretical model involving scattering against plasmons in the constriction.
A. Kristensen, P. E. Lindelof, J. B. Jensen, M. Zaffalon, J. Hollingbery, S. W. Pedersen, J. Nygard, H. Bruus, S. M. Reimann, C. B. Sorensen M. Michel, A. Forchel Journal reference: Physica B 249251, 180 (1998) [ condmat/9807277v1 ] DOI: 10.1016/S09214526(98)000945

Activated Behavior of the 0.7 2(e^2)/h Conductance Anomaly in Quantum
Point Contacts 
Abstract