Transition to Quantum Chaos in Weakly Disordered Graphene Nanoflakes

TL;DR

This paper investigates how weak disorder in graphene nanoflakes causes a transition from regular to chaotic quantum behavior, characterized by changes in energy level statistics.

Contribution

It introduces a universal power-law relationship linking disorder strength to quantum chaos transition across various nanoflake configurations.

Findings

Energy level statistics shift from Poissonian to Wigner distribution with increasing disorder.

Universal power-law maps disorder strength to a single parameter in a random-matrix model.

Transition behavior is consistent across different nanoflake sizes and boundary conditions.

Abstract

We analyze numerically ensembles of tight-binding Hamiltonians describing highly-symmetric graphene nanoflakes with weak diagonal disorder induced by random electrostatic potential landscapes. When increasing the disorder strength, statistical distribution of energy levels evolves from Poissonian to Wigner, indicating the transition to quantum chaos. Power laws with the universal exponent map the disorder strength in nanoflakes of different sizes, boundaries, and microscopic disorder types onto a single parameter in additive random-matrix model.