Symmetry and spectral statistics of the magnetic band structure of a one-dimensional surface superlattice

Abstract

We report a theoretical study of the spectral statistics of a quasi-one-dimensional surface superlattice in perpendicularly applied magnetic fields. The energy-level-spacing distribution and the Dyson–Mehta Δ3 statistic of the magnetic band structure of the system are calculated. The calculations show that for the system with inversion symmetry, the magnetic band structure at the wave vector k = 0 is well described by the statistic derived by a superposition of two independent Gaussian orthogonal ensemble (GOE) statistics. This result is consistent with the fact that the system shows a false time-reversal violation and a real-space symmetry. The calculations show also that when the wave vector k is moved away from the k = 0 point, the statistical properties of the magnetic band structure are excellently described by the GOE statistics. The GOE statistics are also found in the magnetic band structure when the inversion symmetry is removed from the system.