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

One-dimensional proximity superconductivity in the quantum Hall regime

Extensive efforts have been undertaken to combine superconductivity and the quantum Hall effect so that Cooper-pair transport between superconducting electrodes in Josephson junctions is mediated by one-dimensional edge states1-6. This interest has been motivated by prospects of finding new physics, including topologically protected quasiparticles7-9, but also extends into metrology and device applications10-13. So far it has proven challenging to achieve detectable supercurrents through quantum Hall conductors2,3,6. Here we show that domain walls in minimally twisted bilayer graphene14-18 support exceptionally robust proximity superconductivity in the quantum Hall regime, allowing Josephson junctions to operate in fields close to the upper critical field of superconducting electrodes. The critical current is found to be non-oscillatory and practically unchanging over the entire range of quantizing fields, with its value being limited by the quantum conductance of ballistic, strictly one-dimensional, electronic channels residing within the domain walls. The system described is unique in its ability to support Andreev bound states at quantizing fields and offers many interesting directions for further exploration.

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.

Tunable Photoresponse in a Two-Dimensional Superconducting Heterostructure

The photo-induced superconducting phase transition is widely used in probing the physical properties of correlated electronic systems and to realize broadband photodetection with extremely high responsivity. However, such photoresponse is usually insensitive to electrostatic doping due to the high carrier density of the superconductor, restricting its applications in tunable optoelectronic devices. In this work, we demonstrate the gate voltage modulation to the photoresponsivity in a two-dimensional NbSe₂-graphene heterojunction. The superconducting critical current of the NbSe₂ relies on the gate-dependent hot carrier generation in graphene via the Joule heating effect, leading to the observed shift of both the magnitude and peak position of the photoresponsivity spectra as the gate voltage changes. This heating effect is further confirmed by the temperature and laser-power-dependent characterization of the photoresponse. In addition, we investigate the spatially-resolved photocurrent, finding that the superconductivity is inhomogeneous across the junction area. Our results provide a new platform for designing tunable superconducting photodetector and indicate that the photoresponse could be a powerful tool in studying the local electronic properties and phase transitions in low-dimensional superconducting systems.

Phase diagram of superconductivity in the integer quantum Hall regime

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spin polarized electrons on a Hofstadter lattice with nearest-neighbor attractive interaction and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge-invariant observables and a rich phase diagram as a function of the chemical potential, the magnetic field, and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically nontrivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana modes are indicated.

Resonant Scattering in Proximity-Coupled Graphene/Superconducting Mo2 C Heterostructures

The realization of high-quality heterostructures or hybrids of graphene and superconductor is crucial for exploring various novel quantum phenomena and devices engineering. Here, the electronic transport on directly grown high-quality graphene/Mo₂ C vertical heterostructures with clean and sharp interface is comprehensively investigated. Owing to the strong interface coupling, the graphene layer feels an effective confinement potential well imposed by two-dimensional (2D) Mo₂ C crystal. Employing cross junction device geometry, a series of resonance-like magnetoresistance peaks are observed at low temperatures. The temperature and gate voltage dependences of the observed resonance peaks give evidence for geometric resonance of electron cyclotron orbits with the formed potential well. Moreover, it is found that both the amplitude of resonance peaks and conductance fluctuation exhibit different temperature-dependent behaviors below the superconducting transition temperature of 2D Mo₂ C, indicating the correlation of quantum fluctuations and superconductivity. This study offers a promising route toward integrating graphene with 2D superconducting materials, and establishes a new way to investigate the interplay of massless Dirac fermion and superconductivity based on graphene/2D superconductor vertical heterostructures.

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.

Al-Ge-Al Nanowire Heterostructure: From Single-Hole Quantum Dot to Josephson Effect

Superconductor-semiconductor-superconductor heterostructures are attractive for both fundamental studies of quantum phenomena in low-dimensional hybrid systems as well as for future high-performance low power dissipating nanoelectronic and quantum devices. In this work, ultrascaled monolithic Al-Ge-Al nanowire heterostructures featuring monocrystalline Al leads and abrupt metal-semiconductor interfaces are used to probe the low-temperature transport in intrinsic Ge (i-Ge) quantum dots. In particular, demonstrating the ability to tune the Ge quantum dot device from completely insulating, through a single-hole-filling quantum dot regime, to a supercurrent regime, resembling a Josephson field effect transistor with a maximum critical current of 10 nA at a temperature of 390 mK. The realization of a Josephson field-effect transistor with high junction transparency provides a mechanism to study sub-gap transport mediated by Andreev states. The presented results reveal a promising intrinsic Ge-based architecture for hybrid superconductor-semiconductor devices for the study of Majorana zero modes and key components of quantum computing such as gatemons or gate tunable superconducting quantum interference devices.

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.

Quantum Hall-based superconducting interference device

We present a study of a graphene-based Josephson junction with dedicated side gates carved from the same sheet of graphene as the junction itself. These side gates are highly efficient and allow us to modulate carrier density along either edge of the junction in a wide range. In particular, in magnetic fields in the 1- to 2-T range, we are able to populate the next Landau level, resulting in Hall plateaus with conductance that differs from the bulk filling factor. When counter-propagating quantum Hall edge states are introduced along either edge, we observe a supercurrent localized along that edge of the junction. Here, we study these supercurrents as a function of magnetic field and carrier density.

Perfect Crossed Andreev Reflection in Dirac Hybrid Junctions in the Quantum Hall Regime

Perfect crossed Andreev reflection (CAR) is striking for high-efficiency Cooper pair splitting, which bears promising applications in quantum communication. Recent experimental advances have disclosed the way to explore CAR in Dirac fermion systems under ultrastrong magnetic fields. We develop a scattering approach to study quantum-Hall-superconductor-quantum-Hall junctions formed by a two-dimensional time-reversal symmetric Dirac semimetal. We propose two different setups of the hybrid junction in the quantum limit, where only zeroth Landau levels are involved in transport to exploit perfect CAR. In both setups, the CAR probability can reach unity without applying bias voltage and is controllable by the magnetic field strength, the junction width, the length, and the doping of the superconductor. CAR dominates the nonlocal transport and is directly measurable by the differential conductances. We also identify a quantized spin injection per CAR event in one of the two setups. Our proposal is experimentally feasible and will be helpful for exploring high-efficiency Cooper pair splitting and spin injection in Dirac materials.

Next-generation crossover-free quantum Hall arrays with superconducting interconnections

This work presents precision measurements of quantized Hall array resistance devices using superconducting, crossover-free, multiple interconnections as well as graphene split contacts. These new techniques successfully eliminate the accumulation of internal resistances and leakage currents that typically occur at interconnections and crossing leads between interconnected devices. As a result, a scalable quantized Hall resistance array is obtained with a nominal value that is as precise and stable as that from single-element quantized Hall resistance standards.