Theory of wave-packet transport under narrow gaps and spatial textures: Nonadiabaticity and semiclassicality

Abstract

We generalize the celebrated semiclassical wave-packet approach from the adiabatic to the nonadiabatic regime. A unified description covering both of these regimes is particularly desired for systems with spatially varying band structures where band gaps of various sizes are simultaneously present, e.g., in moiré patterns. For a single wave packet, alternative to the previous derivation by Lagrangian variational approach, we show that the same semiclassical equations of motion can be obtained by introducing a spatial-texture-induced force operator similar to the Ehrenfest theorem. For semiclassically computing the current, the ensemble of wave packets based on adiabatic dynamics is shown to well correspond to a phase-space fluid for which the fluid's mass and velocity are two distinguishable properties. This distinction is not inherited to the ensemble of wave packets with the nonadiabatic dynamics. We extend the adiabatic kinetic theory to the nonadiabatic regime by taking into account decoherence, whose joint action with electric field favors certain forms of interband coherence. The steady-state density matrix as a function of the phase-space variables is then phenomenologically obtained for calculating the current. The result, applicable with a finite electric field, expectedly reproduces the known adiabatic limit by taking the electric field to be infinitesimal, and therefore attains a unified description from the adiabatic to the nonadiabatic situations.