Critical level-statistics for weakly disordered graphene

TL;DR

This paper investigates the spectral statistics of weakly disordered graphene, revealing a critical level-statistics behavior akin to the Anderson transition, with implications for quantum transport and edge states.

Contribution

It demonstrates that weak disorder in graphene leads to a unique critical level-statistics, bridging chaotic and localized regimes, and highlights the role of edge states in quantum transport.

Findings

Level-spacing distribution resembles critical point of Anderson transition.

Weak disorder induces a non-chaotic, non-localized spectral regime.

Strong disorder causes graphene to behave as an Anderson insulator.

Abstract

In two dimensions chaotic level-statistics is expected for massless Dirac fermions in the presence of disorder. For weakly disordered graphene flakes with zigzag edges the obtained level-spacing distribution in the Dirac region is neither chaotic (Wigner) nor localized (Poisson) but similar to that at the critical point of the Anderson metal-insulator transition. The quantum transport in finite graphene can occur via critical edge states as in topological insulators, for strong disorder the Dirac region vanishes and graphene behaves as ordinary Anderson insulator.