Equilibrium currents in a Corbino graphene ring

TL;DR

This paper investigates equilibrium currents in a graphene Corbino disk using a tight-binding model that includes spin-orbit coupling, revealing edge state dominance and differences from continuum model predictions.

Contribution

It provides a detailed tight-binding analysis of equilibrium currents in a graphene Corbino ring, validating continuum model assumptions and highlighting edge state effects.

Findings

Dispersion near K points matches continuum model

Edge states dominate charge density at zig-zag edges

Persistent currents differ from traditional continuum predictions

Abstract

We address the description of a graphene Corbino disk in the context of a tight binding approach that includes both kinetic and Rashba spin-orbit coupling due to an external out-of-plane electric field. Persistent equilibrium currents are induced by an external magnetic field breaking time reversal symmetry. By direct diagonalization, we compute the spectrum and focus on the dispersion near the $K$ points at the Fermi level. The dispersion keenly reproduces that of a continuum model in spite of the complexity of the boundary conditions. We validate the assumptions of the continuum model in terms of predominant zig-zag boundaries conditions and weak sub-band coupling. The wave functions displaying the lowest transverse modes are obtained, showing the predominance of edge states with charge density at the zig-zag edges. The persistent charge currents, nevertheless, do not follow the traditional argument of current cancellation from levels below the Fermi level, and thus they depart in the tight-binding from those found in the continuum model.