Andreev reflection in strong magnetic fields

Evidence for chiral supercurrent in quantum Hall Josephson junctions

Hybridizing superconductivity with the quantum Hall (QH) effect has notable potential for designing circuits capable of inducing and manipulating non-Abelian states for topological quantum computation1-3. However, despite recent experimental progress towards this hybridization4-15, concrete evidence for a chiral QH Josephson junction16-the elemental building block for coherent superconducting QH circuits-is still lacking. Its expected signature is an unusual chiral supercurrent flowing in QH edge channels, which oscillates with a specific 2ϕ0 magnetic flux periodicity16-19 (ϕ0 = h/2e is the superconducting flux quantum, where h is the Planck constant and e is the electron charge). Here we show that ultra-narrow Josephson junctions defined in encapsulated graphene nanoribbons exhibit a chiral supercurrent, visible up to 8 T and carried by the spin-degenerate edge channel of the QH plateau of resistance h/2e2 ≈ 12.9 kΩ. We observe reproducible 2ϕ0-periodic oscillations of the supercurrent, which emerge at a constant filling factor when the area of the loop formed by the QH edge channel is constant, within a magnetic-length correction that we resolve in the data. Furthermore, by varying the junction geometry, we show that reducing the superconductor/normal interface length is crucial in obtaining a measurable supercurrent on QH plateaus, in agreement with theories predicting dephasing along the superconducting interface19-22. Our findings are important for the exploration of correlated and fractional QH-based superconducting devices that host non-Abelian Majorana and parafermion zero modes23-32.

Loss and Decoherence at the Quantum Hall-Superconductor Interface

We perform a systematic study of Andreev conversion at the interface between a superconductor and graphene in the quantum Hall (QH) regime. We find that the probability of Andreev conversion from electrons to holes follows an unexpected but clear trend: the dependencies on temperature and magnetic field are nearly decoupled. We discuss these trends and the role of the superconducting vortices, whose normal cores could both absorb and dephase the individual electrons in a QH edge. Our Letter may pave the road to engineering a future generation of hybrid devices for exploiting superconductivity proximity in chiral channels.

Induced Superconducting Pairing in Integer Quantum Hall Edge States

Indium arsenide (InAs) near surface quantum wells (QWs) are promising for the fabrication of semiconductor-superconductor heterostructures given that they allow for a strong hybridization between the two-dimensional states in the quantum well and the ones in the superconductor. In this work, we present results for InAs QWs in the quantum Hall regime placed in proximity of superconducting NbTiN. We observe a negative downstream resistance with a corresponding reduction of Hall (upstream) resistance, consistent with a very high Andreev conversion. We analyze the experimental data using the Landauer-Büttiker formalism, generalized to allow for Andreev reflection processes. We attribute the high efficiency of Andreev conversion in our devices to the large transparency of the InAs/NbTiN interface and the consequent strong hybridization of the QH edge modes with the states in the superconductor.

Magnetotransport in graphene nanoribbons sandwiched by superconductors at side edges

Magnetotransport properties of the graphene nanoribbons (GNR) that are in contact with superconductors at side edges are investigated numerically with respect to oscillations caused by the cyclotron motion. In terms of the modelling, the superconductors are incorporated as superconducting GNRs to make the Andreev reflection at the graphene-superconductor interface almost perfect. The classical commensurability oscillation appears at low magnetic fields where the cyclotron radius is larger than the width of the nanoribbons. A transition to the circumstance dominated by the quantum interference between Andreev- and normal-reflected components takes place when the Andreev reflection probability is reduced by introducing a barrier at the interface. The near perfection of the Andreev reflection enlarges the period of the oscillation associated with skipping orbits a few orders of magnitude in the quantum limit. Chaotic fluctuations emerge furthermore in the regime of Hofstadter's butterfly. The periodicity of a transmission modulation at the onset of the chaos is revealed to change continuously over eight orders of magnitude of the magnetic-field variation. The commensurability and edge-state oscillations are examined additionally for the situations with specular Andreev reflection.

Andreev Reflections in NbN/Graphene Junctions under Large Magnetic Fields

Hybrid superconductor/graphene (SC/g) junctions are excellent candidates for investigating correlations between Cooper pairs and quantum Hall (QH) edge modes. Experimental studies are challenging as Andreev reflections are extremely sensitive to junction disorder, and high magnetic fields are required to form QH edge states. We fabricated low-resistance SC/g interfaces, composed of graphene edge contacted with NbN with a barrier strength of Z ≈ 0.4, that remain superconducting under magnetic fields larger than 18 T. We establish the role of graphene's Dirac band structure on zero-field Andreev reflections and demonstrate dynamic tunability of the Andreev reflection spectrum by moving the boundary between specular and retro Andreev reflections with parallel magnetic fields. Through the application of perpendicular magnetic fields, we observe an oscillatory suppression of the 2-probe conductance in the ν = 4 Landau level attributed to the reduced efficiency of Andreev processes at the NbN/g interface, consistent with theoretical predictions.

Quantum magnetotransport oscillations in graphene nanoribbons coupled to superconductors

Magnetotransport properties of zigzag and armchair graphene nanoribbons that are in contact with superconductors are investigated using a tight-binding model. The cyclotron orbital motion together with the quantum interference under the coexistence of Andreev and normal reflections gives rise to a number of oscillations in characteristic magnetic-field regimes when the superconducting coupling is weak. The oscillations become irregular and/or suppressed as the coupling is made strong. The period of the oscillations differs from that when a nonrelativistic two-dimensional electron gas is employed rather than the graphene sheet. The modifications of the oscillations are attributed to the phase shift associated with the reflection from the graphene-superconductor interface. The presence of a magnetic field suppresses the quantum blocking of Andreev transmission, which occurs for the edge mode of zigzag nanoribbons, in the same way regardless of it being induced by the Andreev retro- or specular reflection.

Commensurability and quantum interference magnetotransport oscillations in a two-dimensional electron gas sandwiched by superconductors

Magnetic-field dependence of the transport properties of ballistic two-dimensional electrons in a planar superconductor-normal-conductor-superconductor structure is numerically investigated. In the circumstance where the Andreev reflection from the normal-conductor-superconductor interfaces is almost perfect, two oscillatory behaviors occur for magnetic fields higher and lower than that for the coincidence of the cyclotron diameter with the separation between the superconductors. The oscillation period for the former and latter cases is proportional to the magnetic field and inverse of the magnetic field, respectively. The low-field oscillation originates from commensurability-driven guiding of Andreev-reflected trajectories along the interfaces between the normal conductor and the superconductors. If the Andreev reflection probability is considerably less than unity, the commensurability oscillation is suppressed in amplitude and is dwarfed by additionally emerged oscillations originating from the quantum interference between the Andreev- and normal-reflected components.

Inter-Landau-level Andreev Reflection at the Dirac Point in a Graphene Quantum Hall State Coupled to a NbSe_{2} Superconductor

Superconductivity and the quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of the quantum Hall effect with a superconductor can provide fertile ground for realizing exotic topological excitations such as non-Abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two-dimensional niobium diselenide (NbSe_{2}) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau-level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles.

Proximity coupling in superconductor-graphene heterostructures

This review discusses the electronic properties and the prospective research directions of superconductor-graphene heterostructures. The basic electronic properties of graphene are introduced to highlight the unique possibility of combining two seemingly unrelated physics, superconductivity and relativity. We then focus on graphene-based Josephson junctions, one of the most versatile superconducting quantum devices. The various theoretical methods that have been developed to describe graphene Josephson junctions are examined, together with their advantages and limitations, followed by a discussion on the advances in device fabrication and the relevant length scales. The phase-sensitive properties and phase-particle dynamics of graphene Josephson junctions are examined to provide an understanding of the underlying mechanisms of Josephson coupling via graphene. Thereafter, microscopic transport of correlated quasiparticles produced by Andreev reflections at superconducting interfaces and their phase-coherent behaviors are discussed. Quantum phase transitions studied with graphene as an electrostatically tunable 2D platform are reviewed. The interplay between proximity-induced superconductivity and the quantum-Hall phase is discussed as a possible route to study topological superconductivity and non-Abelian physics. Finally, a brief summary on the prospective future research directions is given.

Topological π Junctions from Crossed Andreev Reflection in the Quantum Hall Regime

We consider a two-dimensional electron gas (2DEG) in the quantum Hall regime in the presence of a Zeeman field, with the Fermi level tuned to a filling factor of ν=1. We show that, in the presence of spin-orbit coupling, contacting the 2DEG with a narrow strip of an s-wave superconductor produces a topological superconducting gap along the contact as a result of crossed Andreev reflection (CAR) processes across the strip. The sign of the topological gap, controlled by the CAR amplitude, depends periodically on the Fermi wavelength and strip width and can be externally tuned. An interface between two halves of a long strip with topological gaps of opposite sign implements a robust π junction, hosting a pair of Majorana zero modes that do not split despite their overlap. We show that such a configuration can be exploited to perform protected non-Abelian tunnel-braid operations without any fine tuning.

Equal-Spin Andreev Reflection on Junctions of Spin-Resolved Quantum Hall Bulk State and Spin-Singlet Superconductor

The recent development of superconducting spintronics has revealed the spin-triplet superconducting proximity effect from a spin-singlet superconductor into a spin-polarized normal metal. In addition recently superconducting junctions using semiconductors are in demand for highly controlled experiments to engineer topological superconductivity. Here we report experimental observation of Andreev reflection in junctions of spin-resolved quantum Hall (QH) states in an InAs quantum well and the spin-singlet superconductor NbTi. The measured conductance indicates a sub-gap feature and two peaks on the outer side of the sub-gap feature in the QH plateau-transition regime increases. The observed structures can be explained by considering transport with Andreev reflection from two channels, one originating from equal-spin Andreev reflection intermediated by spin-flip processes and second arising from normal Andreev reflection. This result indicates the possibility to induce the superconducting proximity gap in the the QH bulk state, and the possibility for the development of superconducting spintronics in semiconductor devices.

Propagation of superconducting coherence via chiral quantum-Hall edge channels

Recently, there has been significant interest in superconducting coherence via chiral quantum-Hall (QH) edge channels at an interface between a two-dimensional normal conductor and a superconductor (N–S) in a strong transverse magnetic field. In the field range where the superconductivity and the QH state coexist, the coherent confinement of electron- and hole-like quasiparticles by the interplay of Andreev reflection and the QH effect leads to the formation of Andreev edge states (AES) along the N–S interface. Here, we report the electrical conductance characteristics via the AES formed in graphene–superconductor hybrid systems in a three-terminal configuration. This measurement configuration, involving the QH edge states outside a graphene–S interface, allows the detection of the longitudinal and QH conductance separately, excluding the bulk contribution. Convincing evidence for the superconducting coherence and its propagation via the chiral QH edge channels is provided by the conductance enhancement on both the upstream and the downstream sides of the superconducting electrode as well as in bias spectroscopy results below the superconducting critical temperature. Propagation of superconducting coherence via QH edge states was more evident as more edge channels participate in the Andreev process for high filling factors with reduced valley-mixing scattering.

Supercurrent in the quantum Hall regime

A promising route for creating topological states and excitations is to combine superconductivity and the quantum Hall (QH) effect. Despite this potential, signatures of superconductivity in the QH regime remain scarce, and a superconducting current through a QH weak link has been challenging to observe. We demonstrate the existence of a distinct supercurrent mechanism in encapsulated graphene samples contacted by superconducting electrodes, in magnetic fields as high as 2 tesla. The observation of a supercurrent in the QH regime marks an important step in the quest for exotic topological excitations, such as Majorana fermions and parafermions, which may find applications in fault-tolerant quantum computing.

Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures

Search for Majorana fermions renewed interest in semiconductor–superconductor interfaces, while a quest for higher-order non-Abelian excitations demands formation of superconducting contacts to materials with fractionalized excitations, such as a two-dimensional electron gas in a fractional quantum Hall regime. Here we report induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures and development of highly transparent semiconductor–superconductor ohmic contacts. Supercurrent with characteristic temperature dependence of a ballistic junction has been observed across 0.6 μm, a regime previously achieved only in point contacts but essential to the formation of well separated non-Abelian states. High critical fields (>16 T) in NbN contacts enables investigation of an interplay between superconductivity and strongly correlated states in a two-dimensional electron gas at high magnetic fields.

Superconductivity has been induced in 2D electron gases, but high-field interplay between it and quantum Hall edge states remains elusive. Here the authors reach this regime by growing transparent superconducting contacts in GaAs, reporting modification of resistance in the quantum Hall regime.

Snake trajectories in ultraclean graphene p-n junctions

Snake states are trajectories of charge carriers curving back and forth along an interface. There are two types of snake states, formed by either inverting the magnetic field direction or the charge carrier type at an interface. The former has been demonstrated in GaAs–AlGaAs heterostructures, whereas the latter has become conceivable only with the advance of ballistic graphene where a gap-less p–n interface governed by Klein tunnelling can be formed. Such snake states were hidden in previous experiments due to limited sample quality. Here we report on magneto-conductance oscillations due to snake states in a ballistic suspended graphene p–n junction, which occur already at a very small magnetic field of 20 mT. The visibility of 30% is enabled by Klein collimation. Our finding is firmly supported by quantum transport simulations. We demonstrate the high tunability of the device and operate it in different magnetic field regimes.

Snake states describe electron trajectories that curve along an interface where the charge is inverted. Here, the authors investigate electronic transport in a ballistic graphene p–n junction and observe striking conductance oscillations that are a signature of these unusual states.

Majorana fermions from Landau quantization in a superconductor and topological-insulator hybrid structure

We show that the interplay of cyclotron motion and Andreev reflection experienced by massless-Dirac-like charge carriers in topological-insulator surface states generates a Majorana-particle excitation. On the basis of an envelope-function description of the Dirac-Andreev edge states, we discuss the kinematic properties of the Majorana mode and find them to be tunable by changing the superconductor's chemical potential and/or the magnitude of the perpendicular magnetic field. Our proposal opens up new possibilities for studying Majorana fermions in a controllable setup.

Quantum Hall effect in graphene with superconducting electrodes

We have realized an integer quantum Hall system with superconducting contacts by connecting graphene to niobium electrodes. Below their upper critical field of 4 T, an integer quantum Hall effect coexists with superconductivity in the leads but with a plateau conductance that is larger than in the normal state. We ascribe this enhanced quantum Hall plateau conductance to Andreev processes at the graphene-superconductor interface leading to the formation of so-called Andreev edge-states. The enhancement depends strongly on the filling-factor and is less pronounced on the first plateau due to the special nature of the zero energy Landau level in monolayer graphene.

Detection of valley polarization in graphene by a superconducting contact

Because the valleys in the band structure of graphene are related by time-reversal symmetry, electrons from one valley are reflected as holes from the other valley at the junction with a superconductor. We show how this Andreev reflection can be used to detect the valley polarization of edge states produced by a magnetic field. In the absence of intervalley relaxation, the conductance GNS=(2e2/h)(1-cosTheta) of the junction on the lowest quantum Hall plateau is entirely determined by the angle Theta between the valley isospins of the edge states approaching and leaving the superconductor. If the superconductor covers a single edge, Theta=0 and no current can enter the superconductor. A measurement of GNS then determines the intervalley relaxation time.

Andreev reflection at high magnetic fields: evidence for electron and hole transport in edge states

We have studied magnetotransport in arrays of niobium filled grooves in an InAs/Al(x)Ga(1-x)Sb heterostructure. The critical field of up to 2.6 T permits one to enter the quantum Hall regime. In the superconducting state, we observe strong magnetoresistance oscillations, whose amplitude exceeds the Shubnikov-de Haas oscillations by a factor of about 2, when normalized to the background. Additionally, we find that above a geometry-dependent magnetic field value the sample in the superconducting state has a higher longitudinal resistance than in the normal state. Both observations can be explained with edge channels populated with electrons and Andreev-reflected holes.