Quantum chaos in disordered graphene

TL;DR

This study numerically investigates electronic state statistics in disordered graphene, revealing a transition from quantum chaotic to localized behavior depending on disorder strength and sample geometry.

Contribution

It provides the first detailed numerical analysis of level statistics in disordered graphene across various geometries and disorder regimes.

Findings

Weak disorder induces Wigner level-spacing distribution.

Strong disorder leads to Anderson localization with Poisson statistics.

Chaotic diffusive behavior is common in realistic samples.

Abstract

We have studied numerically the statistics for electronic states (level-spacings and participation ratios) from disordered graphene of finite size, described by the aspect ratio $W/L$ and various geometries, including finite or torroidal, chiral or achiral carbon nanotubes. Quantum chaotic Wigner energy level-spacing distribution is found for weak disorder, even infinitesimally small disorder for wide and short samples ($W/L>>1$), while for strong disorder Anderson localization with Poisson level-statistics always sets in. Although pure graphene near the Dirac point corresponds to integrable ballistic statistics chaotic diffusive behavior is more common for realistic samples.