Chaotic electron motion in superlattices. Quantum-classical correspondence of the structure of eigenstates and LDOS

We investigate the classical-quantum correspondence for the motion of a particle in a 2D infinitely long channel with periodic modulated boundaries. Its classical dynamics undergoes the generic transition to chaos of Hamiltonian systems as the amplitude of the modulation is increased. We show that in the case of strong chaotic motion, the classical counterparts of the structure of eigenstates (SES) and local density of states (LDOS) in energy space reveal an excellent agreement with the quantum quantities. This correspondence allowed us to understand important features of the SES and LDOS in terms of classical trajectories. We also show that certain localization measures in energy space are very useful in the characterization of individual states and their transport properties. We find that in any given interval of energy, there are wild variations of the localizations measures and these can be explained by the existence of two length scales, typical of 2D systems.