Chaotic Electron Motion in Superlattices. Quantum-Classical Correspondence of the Structure of Eigenstates and LDOS

We investigate the classical-quantum correspondence for particle motion in a superlattice in the form of a 2D 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 for strong chaotic motion, the classical counterpart of the structure of eigenstates (SES) in energy space reveals an excellent agreement with the quantum one. This correspondence allows us to understand important features of the SES in terms of classical trajectories. We also show that for typical 2D modulated waveguides there exist, at any energy range, extremely localized eigenstates (in energy) which are practically unperturbed by the modulation. These states contribute to the strong fluctuations around the classical SES. The approach to the classical limit is discussed.