Landau-Zener tunneling in 2D periodic structures in the presence of a gauge field I: Tunneling rates

TL;DR

This paper extends Landau-Zener tunneling theory to two-dimensional periodic structures with gauge fields, analyzing tunneling rates in quantum particles under Hall configuration using semi-analytical methods.

Contribution

It generalizes Landau-Zener tunneling theory to include non-zero gauge fields in 2D structures, providing a semi-analytical approach to calculate tunneling rates.

Findings

Derived generalized Landau-Zener tunneling rates for 2D systems with gauge fields.

Developed a semi-analytical method using truncated Floquet matrices.

Provided insights into interband tunneling in Hall configurations.

Abstract

We study the interband Landau-Zener tunneling of a quantum particle in the Hall configuration, i.e., in the presence of normal to the lattice plane gauge field (for example, magnetic field for a charged particle) and in-plane potential field (electric field for a charged particle). The interband tunneling is induced by the potential field and for vanishing gauge field is described by the common Landau-Zener theory. We generalize this theory for non-zero gauge field. The depletion rates of low-energy bands are calculated by using semi-analytical method of the truncated Floquet matrix.