Manifestation of quantum chaos in the spectra of quasi-one-dimensional surface superlattices

Abstract

Two statistical properties, namely, the energy level spacing distribution and the Dyson-Mehta statistics, are reported for the energy band structure of a confined, surface superlattice in perpendicularly applied magnetic fields. Time-reversal (T) symmetry is broken in the system. However, the system is invariant under the anti-unitary combination of symmetric operations which includes T, leading to what is called false time-reversal violation. For the wave vector k not in close vicinity of the symmetrical points in k-space, the statistical properties of the band structure at sufficiently strong magnetic fields are found to be described by Gaussian orthogonal ensemble (GOE) statistics. This result is a clear manifestation of quantum chaos in the system and is in agreement with the prediction that the false time-reversal violation suffices to give the energy spectra the properties of the GOE, instead of the Gaussian unitary ensemble. The spectra are found to deviate from the GOE statistics when the wave vector k is moved towards the symmetrical points in k-space and/or the magnetic field towards B = 0. This is because in these limit cases, the system is invariant under at least one geometric, symmetrical operation and hence spectral degeneracy becomes possible. The implications of this work for experiments are also discussed.