Critical delocalization of chiral zero energy modes in graphene

TL;DR

This paper demonstrates through large-scale quantum transport calculations that zero energy modes in graphene with chiral-symmetric disorder exhibit critical delocalization, challenging previous localization expectations.

Contribution

The study provides the first large-scale numerical evidence that zero energy modes in chiral graphene remain delocalized and metallic, confirming theoretical predictions beyond weak-coupling regimes.

Findings

Kubo dc conductivity matches 4e^2/πh within 1% accuracy

Unprecedented robust metallic regime in disordered graphene

Supports field-theoretical predictions for BDI class beyond weak-coupling

Abstract

Graphene subjected to chiral-symmetric disorder is believed to host zero energy modes (ZEMs) resilient to localization, as suggested by the renormalization group analysis of the underlying nonlinear sigma model. We report accurate quantum transport calculations in honeycomb lattices with in excess of $10^{9}$ sites and fine meV resolutions. The Kubo dc conductivity of ZEMs induced by vacancy defects (chiral BDI class) is found to match $4e^{2}/\pi h$ within 1% accuracy, over a parametrically wide window of energy level broadenings and vacancy concentrations. Our results disclose an unprecedentedly robust metallic regime in graphene, providing strong evidence that the early field-theoretical picture for the BDI class is valid well beyond its controlled weak-coupling regime.