Spectral statistics of weakly disordered triangular graphene flakes with zigzag edges are revisited. Earlier, we have found numerically that such systems may show spectral fluctuations of Gaussian unitary ensemble (GUE), signaling the time‐reversal symmetry (TRS) breaking at zero magnetic field, accompanied by approximate twofold valley degeneracy of each energy level. Atomic‐scale disorder induces the scattering of charge carriers between the valleys and restores the spectral fluctuations of Gaussian orthogonal ensemble (GOE). A simplified description of such a nonstandard GUE‒GOE transition, employing the mixed ensemble of 4 × 4 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.
Part of the book: Recent Advances in Graphene Research