SU(4) Symmetry Breaking and Induced Superconductivity in Graphene Quantum Hall Edges

TL;DR

This paper investigates how SU(4) symmetry breaking in graphene's quantum Hall edge modes influences their transport properties and enables potential realization of topological superconductivity with Majorana modes.

Contribution

It demonstrates the impact of symmetry breaking on edge mode transport and proposes conditions for realizing topological superconductivity in graphene QH edges near a superconductor.

Findings

Symmetry breaking lifts Landau level degeneracy affecting edge transport.

Proposes a method to realize 1D topological superconductors supporting Majoranas.

Estimates the topological gap based on interface properties.

Abstract

In graphene, the approximate SU(4) symmetry associated with the spin and valley degrees of freedom in the quantum Hall (QH) regime is reflected in the 4-fold degeneracy of graphene's Landau levels (LL's). Interactions and the Zeeman effect break such approximate symmetry and lift the corresponding degeneracy of the LLs. We study how the breaking of the approximate SU(4) symmetry affects the properties of graphene's QH edge modes located in proximity to a superconductor. We show how the lifting of the 4-fold degeneracy qualitatively modifies the transport properties of the QH-superconductor heterojunction. For the zero LL, by placing the edge modes in proximity to a superconductor, it is in principle possible to realize a 1D topological superconductor supporting Majoranas in the presence of sufficiently strong Zeeman field. We estimate the topological gap of such a topological superconductor and relate it to the properties of the QH-superconductor interface.