Proximity-induced superconductivity in Landau-quantized graphene monolayers

Abstract

We consider massless Dirac fermions in a graphene monolayer in the ballistic limit, subject to both a perpendicular magnetic field B and a proximity-induced pairing gap ∆. When the chemical potential is at the Dirac point, our exact solution of the Bogoliubov-de Gennes equation yields ∆-independent relativistic Landau levels. Since eigenstates depend on ∆, many observables nevertheless are sensitive to pairing, e.g., the local density of states or the edge state spectrum. By solving the problem with an additional in-plane electric field, we also discuss how snake states are influenced by a pairing gap.

Current correlations of Cooper-pair tunneling into a quantum Hall system

“…In the recent past, it has become possible to investigate such transport problems not only between identical ballistic chiral QH states but also between distinct systems, such as QH edge states and superconductors, both theoretically [61][62][63][64][65][66][67][68][69][70] and experimentally [19,20,22,[71][72][73][74]. This line of research is particularly relevant for the creation of parafermion bound states, non-Abelian quasiparticles with potential application in topological quantum computation [75][76][77][78][79][80][81][82][83][84].…”

Effects of Lorentz violation in superconductivity

“…Although initially thought of as a phenomenological theory, the GL theory can be interpreted as a limiting case of the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity [18]. Superconductivity in Weyl semimetals [19][20][21] as well as in carbon-based nanostructures such as graphene and fullerene [22,23] are topics often addressed in the literature due to their possible applications in technological improvement. However the study of superconductivity in a more theoretical framework such as superconductivity in astrophysics [24,25], cosmology [26,27] and in high energy physics [28,29], for example, has been intensively discussed in the last years.…”

Chiral quasiparticle tunneling between quantum Hall edges in proximity with a superconductor

“…Experimentally, this was prompted by several groups successfully making high-transparency type II superconducting contacts to both encapsulated graphene and III-V semiconductor heterostructures [1][2][3][4][5][6][7][8][9][10] . Meanwhile, theoretical works have predicted multiple exciting phenomena in structures combining the quantum Hall effect and superconductivity [11][12][13][14][15][16][17][19][20][21][22][23][24][25][26][27][28][29][30][31] . In particular, it is expected that Andreev edge states (AES) -hybrid modes involving a linear superposition of electron and hole states -should be formed at these QH-SC interfaces 9,[14][15][16][17] .…”