Proximity-induced superconductivity in Landau-quantized graphene monolayers

TL;DR

This paper investigates how proximity-induced superconductivity affects Landau-quantized graphene, revealing that certain Landau levels are unaffected by pairing while observables like the local density of states are sensitive to it.

Contribution

The study provides an exact solution for Dirac fermions in graphene under magnetic and pairing fields, highlighting the independence of Landau levels from the pairing gap at the Dirac point.

Findings

Landau levels are independent of the pairing gap at the Dirac point.

Observable properties like local density of states depend on the pairing gap.

Edge states and snake states are influenced by the proximity-induced pairing.

Abstract

We consider massless Dirac fermions in a graphene monolayer subject to both a perpendicular magnetic field $B$ and a proximity-induced pairing gap $\Delta$. When the chemical potential is at the Dirac point, our exact solution of the Bogoliubov-de Gennes equation yields $\Delta$-independent relativistic Landau levels. Since eigenstates depend on $\Delta$, 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.