# Chiral anomaly and anomalous finite-size conductivity in graphene

## TL;DR

This paper explores how the chiral anomaly in graphene leads to an unusual finite-size correction to conductivity, which can be experimentally observed and is distinct from boundary mode effects.

## Contribution

It demonstrates that the chiral anomaly causes a positive finite-size correction to conductivity in graphene, inversely proportional to the square of the width, revealing a measurable signature.

## Key findings

- Finite-size correction to conductivity is positive and inversely proportional to W^2.
- Chiral anomaly manifests as an anomalous finite-size conductivity in graphene.
- The effect is distinct from boundary mode contributions and is experimentally detectable.

## Abstract

Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two pairs of massless two-dimensional Dirac fermions in the absence of or with negligible spin-orbit coupling. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of zigzag nanoribbon. The Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges at different valleys can be realized in a confined ribbon of finite width. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and goes inversely with the square of the lateral dimension W, which is different from the finite-size correction inversely with W from boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and is measurable experimentally.