Dynamic localization of lattice electrons under time dependent electric and magnetic fields

TL;DR

This paper derives conditions for dynamic localization of electrons in a one-dimensional lattice under time-dependent electric and magnetic fields, revealing frequency mixing effects and phase tuning impacts.

Contribution

It introduces a method using characteristics to analyze dynamic localization under combined time-dependent electric and magnetic fields, incorporating Bessel functions and phase effects.

Findings

Localization conditions expressed via Bessel function sums.

Frequency mixing effects influence localization.

Phase tuning simplifies the localization criteria.

Abstract

Applying the method of characteristics leads to wavefunctions and dynamic localization conditions for electrons on the one dimensional lattice under perpendicular time dependent electric and magnetic fields. Such conditions proceed again in terms of sums of products of Bessel functions of the first kind. However, this time one deals with both the number of magnetic flux quanta times $\pi $ and the quotients between the Bloch frequency and the ones characterizing competing fields. Tuning the phases of time dependent modulations leads to interesting frequency mixing effects providing an appreciable simplification of dynamic localization conditions one looks for. The understanding is that proceeding in this manner, the time dependent superposition mentioned above gets reduced effectively to the influence of individual ac-fields exhibiting mixed frequency quotients. Besides pure field limits and superpositions between uniform electric and time dependent magnetic fields, parity and periodicity effects have also been discussed.