# The influence of anti-chiral edge states on Andreev reflection in graphene-superconductor junction

## TL;DR

This paper investigates how anti-chiral edge states influence Andreev reflection in a graphene-superconductor junction with broken time reversal symmetry, revealing asymmetric retro-reflection behavior due to edge-bulk scattering.

## Contribution

It introduces a novel analysis of Andreev reflection in graphene with anti-chiral edge states, highlighting asymmetric retro-reflection caused by broken time reversal symmetry.

## Key findings

- Retro-reflection coefficient is symmetric about incident energy in two-terminal devices.
- Specular Andreev reflection coefficient remains symmetric, consistent with previous reports.
- Retro-reflection exhibits unexpected asymmetry due to anti-chiral edge states.

## Abstract

Using the tight binding model and the non-equilibrium Green function method, we study Andreev reflection in graphene-superconductor junction, where graphene has two nonequal Dirac Cones split in energy and therefore time reversal symmetry is broken. Due to the anti-chiral edge states of the current graphene model, an incident electron travelling along the edges makes distinct contribution to Andreev reflections. In a two-terminal device, because Andreev retro-reflection is not allowed for just the anti-chiral edges, in this case the mutual scattering between edge and bulk states is necessary, which leads that the coefficient of Andreev retro-reflection is always symmetrical about the incident energy. In a four-terminal junction, however, the edges are parallel to the interface of superconductor and graphene, so at the interface an incident electron travelling along the edges can be retro-reflected as a hole into bulk modes, or specularly reflected as a hole into anti-chiral edge states again. It is noted that, the coefficient of specular Andreev reflection keeps symmetric as to the incident energy of electron which is consistent with the reported results before, however the coefficient of Andreev retro-reflection shows an unexpected asymmetrical behavior due to the presence of anti-chiral edge states. Our results present some new ideas to study the anti-chiral edge modes and Andreev reflection for a graphene model with the broken time reversal symmetry.