Effective model for Majorana modes in graphene

TL;DR

This paper derives a low-energy effective Hamiltonian for graphene-superconductor interfaces in the quantum Hall regime, highlighting the importance of normal reflections for understanding Majorana modes.

Contribution

It provides a first-principles derivation of the effective model for graphene-superconductor interfaces, incorporating normal reflections often neglected in prior models.

Findings

Normal reflections are crucial for accurate low-energy descriptions.

The effective Hamiltonian aligns with tight-binding simulations.

The model facilitates experimental control of Majorana modes.

Abstract

It was recently proposed that the interface between a graphene nanoribbon in the canted antiferromagnetic quantum Hall state and a s-wave superconductor may present topological superconductivity, resulting in the appearance of Majorana zero modes. However, a description of the low-energy physics in terms of experimentally controllable parameters was still missing. Starting from a mean-field continuum model for graphene in proximity to a superconductor, we derive the low-energy effective Hamiltonian describing the interface of this heterojunction from first principles. A comparison between tight-binding simulations and analytical calculations with effective masses suggests that normal reflections at the interface must be considered in order to fully describe the low-energy physics.