Nonstandard transition GUE-GOE for random matrices and spectral statistics of graphene nanoflakes

TL;DR

This paper investigates the spectral statistics of graphene nanoflakes, revealing a nonstandard GUE-GOE transition influenced by size and defects, with implications for understanding symmetry breaking in quantum systems.

Contribution

It introduces a numerical analysis of large matrices in a mixed ensemble to model spectral fluctuations in disordered graphene flakes, extending previous simplified models.

Findings

Spectral fluctuations depend on size and defect density.

A phase diagram shows conditions for GUE signatures.

Scaling laws relate physical parameters to spectral statistics.

Abstract

Spectral statistics of weakly-disordered triangular graphene flakes with zigzag edges are revisited. Earlier, we have found numerically that such systems may shown spectral fluctuations of GUE, signalling the time-reversal symmetry breaking at zero magnetic field, accompanied by approximate twofold valley degeneracy of each energy level [Phys. Rev. B 85, 245424 (2012)]. Atomic-scale disorder induce the scattering of charge carriers between the valleys and restores the spectral fluctuations of GOE. A simplified description of such a nonstandard GUE-GOE transition, employing the mixed ensemble of 4x4 real symmetric matrices was also proposed. Here we complement our previous study by analyzing numerically the spectral fluctuations of large matrices belonging the same mixed ensemble. Resulting scaling laws relate the ensemble parameter to physical size and the number of atomic-scale defects in graphene flake. A phase diagram, indicating the regions in which the signatures of GUE may by observable in the size-doping parameter plane, is presented.