Uniform current in graphene strip with zigzag edges

TL;DR

This paper derives a rigorous relation for current density in graphene strips with zigzag edges, revealing that despite edge localization, the current density is uniformly distributed across the strip.

Contribution

It provides a new theoretical derivation explaining why current density is uniform in zigzag-edged graphene strips, resolving previous numerical observations.

Findings

Current density is uniform across the graphene strip.

Edge states do not concentrate current at the edges.

Theoretical derivation clarifies previous numerical results.

Abstract

Graphene exhibits zero-gap massless-Dirac fermion and zero density of states at E = 0. These particles form localized states called edge states on finite width strip with zigzag edges at E = 0. Naively thinking, one may expect that current is also concentrated at the edge, but Zarbo and Nikolic numerically obtained a result that the current density shows maximum at the center of the strip. We derive a rigorous relation for the current density, and clarify the reason why the current density of edge state has a maximum at the center.