Wannier-Stark states in double-periodic lattices II: two-dimensional lattices

TL;DR

This paper investigates the Wannier-Stark spectrum in two-dimensional double-periodic lattices, revealing how the energy band structure influences wave packet spreading and exhibits fractal behavior depending on the static field orientation.

Contribution

It provides asymptotic formulas for energy bands in various field regimes and explores the fractal nature of wave-packet dispersion in 2D lattices.

Findings

Energy band structure affects wave packet spreading rates.

Wave-packet dispersion exhibits fractal dependence on field orientation.

Asymptotic expressions for energy bands in different static field regimes.

Abstract

We analyze the Wannier-Stark spectrum of a quantum particle in tilted two-dimensional lattices with the Bloch spectrum consisting of two subbands, which could be either separated by a finite gap or connected at the Dirac points. For rational orientations of the static field given by an arbitrary superposition of the translation vectors the spectrum is a ladder of energy bands. We obtain asymptotic expressions for the energy bands in the limit of large and weak static fields and study them numerically for intermediate field strength. We show that the structure of energy bands determines the rate of spreading of a localized wave packets which is the quantity measured in laboratory experiments. It is shown that wave-packet dispersion becomes a fractal function of the field orientation in the long-time regime of ballistic spreading.