Supercurrent in the quantum Hall regime

Abstract

A novel promising route for creating topological states and excitations is to combine superconductivity and the quantum Hall (QH) effect [1,2] . Despite this potential, signatures of superconductivity in the quantum Hall regime remain scarce [5][6][7][8][9][10][11] , and a superconducting current through a QH weak link has so far eluded experimental observation. Here we demonstrate the existence of a new type of supercurrent-carrying states in a QH region at magnetic fields as high as 2 Tesla. The observation of supercurrent in the quantum Hall 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 computations.1 arXiv:1512.09083v1 [cond-mat.mes-hall] Dec 2015The interplay of the quantum Hall effect with superconductivity is expected to result in novel excitations with non-trivial braiding statistics such as Majorana fermions and non-abelian Majorana anyons [1][2][3][4] . When a quantum Hall region is contacted by two superconducting electrodes, the gapped QH bulk prevents the flow of a supercurrent. However, it was predicted more than 20 years ago that the supercurrent may still be mediated by QH edge states [12] . Due to its chiral nature, a single edge can only conduct charge carriers in one direction, so both edges have to be involved in establishing supercurrent between the two contacts. This situation is fundamentally different from the Josephson junctions made of two-dimensional topological insulators, where each edge can support its own supercurrent [13][14][15][16] . Indeed, contrary to the case of topological insulators, the magnetic field in the QH regime breaks time-reversal symmetry, which is essential for the s-wave pairing of conventional superconductors. Nonetheless, we observe a robust supercurrent in the quantum Hall regime, which we attribute to an unconventional form of Andreev bound states circulating along the perimeter of the QH region and involving electron and hole trajectories separated by several micrometers. We performed transport measurements on four Josephson junctions (J 1−4 ) made of graphene encapsulated in boron nitride and contacted by electrodes made of a molybdenum-rhenium alloy [Fig. 1a] [11] , a type II superconductor with a high upper critical field of H c2 =8 T. The high quality of these heterostructures allowed us to observe Fabry-Perot oscillations of the junctions' resistance and critical current, indicating that the transmission of charge carriers between the contacts is ballistic [17] . The supercurrent is uniformly distributed along the width of the contacts, as evidenced by the regular Fraunhofer pattern [18] measured at small magnetic fields [17] . All junctions demonstrate supercurrent in the QH regime; for consistency, we choose to present data measured on sample J 1 , which has a distance between contacts L = 0.3 µm and a width of the contacts W = 2.4µm (see Figure 1b). Recent preprint reported on the observation of supercurrent ...

Tunnelling spectroscopy of Andreev states in graphene

“…The combined effects of disorder, geometry, and Fermi energy offer many opportunities to investigate Andreev physics in different mesoscopic superconductivity regimes. Moreover, as graphene's extended 2D nature enables one to combine superconductivity and the quantum Hall effect 29 , this platform is promising for the detection of Majorana modes 18 , key ingredients for topologically protected quantum computation.…”

“…The way ABS form in graphene still remains an open question, especially around the neutrality point, where its unique electronic spectrum should give rise to specular Andreev reflections 27,30 and potentially to exotic ABS. Interest in such a spectroscopy has increased with recent proposals for hosting Majorana modes [16][17][18] within proximitized graphene operated in the quantum Hall regime 29 .…”

“…These properties, combined with the ability to control the number of conduction channels with a gate voltage, make graphene an ideal test-bed for exploring Andreev physics in two dimensions (2D). Although the superconducting proximity effect in graphene has attracted considerable research interest [19][20][21][22][23][24][25][26][27][28][29] , most of the experimental studies have been limited to transport measurements of dissipationless supercurrent in graphene-based (S-G-S) Josephson junctions. Accessing the energy domain while controlling the superconducting phase difference is crucial for probing ABS, and it has been performed in just a few systems, such as silver wires 9 , carbon nanotubes 10 , semiconductor nanowires 11 , and atomic breakjunctions 12,13 .…”

Charge2e/3Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States

“…Recent experiments have demonstrated advances in coupling superconductors to semiconductor 2DEGS [45,46], e.g. through epitaxial growth [46] and to graphene in the quantum Hall regime [47].The edge of the bilayer FQH system described above now consists of counterpropagating chiral Luttinger liquids, described by the following Lagrangian density [48]:φ I , for I = 1, 2 are counterpropagating chiral scalar fields satisfying a periodicity condition φ I ∼ φ I + 2π. The electron annihilation operator on each edge is given by Ψ 1↑ ∼ e i3φ 1↑ , Ψ 2↓ ∼ e i3φ 3↓ , the charge e/3 quasiparticle in each layer is given by e iφ I , and the charge density in each layer is ρ I = (−1) I 2π ∂ x φ I .…”

“…Recent experiments have demonstrated advances in coupling superconductors to semiconductor 2DEGS [45,46], e.g. through epitaxial growth [46] and to graphene in the quantum Hall regime [47].…”