Nonstandard transition GUE-GOE for random matrices and spectral statistics of graphene nanoflakes
arXiv:1604.03783 · doi:10.5772/64240
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.
Typos corrected; hyperlinked references. 19 pages, 6 figures. A chapter submitted to "2D Materials", ISBN 978-953-51-4813-5, to be published by InTechOpen
References in corpus (15)
- Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Chaotic Dirac billiard in graphene quantum dots
- The electronic properties of bilayer graphene
- Quantum-limited shot noise in graphene
- Transport measurements across a tunable potential barrier in graphene
- Shot Noise in Ballistic Graphene
- Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
- Symmetry Classes in Graphene Quantum Dots: Universal Spectral Statistics, Weak Localization, and Conductance Fluctuations
- Conductivity and Fano factor in disordered graphene
- Conformal mapping and shot noise in graphene
- Pseudo-diffusive magnetotransport in graphene
- Terahertz Quantum Hall Effect in a Topological Insulator
- Pseudodiffusive conductance, quantum-limited shot noise, and Landau-level hierarchy in biased graphene bilayer
- Nonstandard transition GUE-GOE for random matrices and spectral statistics of graphene nanoflakes