Non-perturbative electron dynamics in crossed fields

TL;DR

This paper investigates non-perturbative electron dynamics in double quantum wells under intense AC electric and tilted magnetic fields, revealing dynamic localization phenomena, hidden symmetries, and complex return time behaviors across frequency ranges.

Contribution

It introduces a non-perturbative Floquet-Fourier approach to analyze electron localization and spectral crossings in crossed fields, uncovering hidden symmetries and detailed dynamical behaviors.

Findings

Dynamic localization occurs at specific field values even with non-zero parallel magnetic field.

High-frequency regimes reproduce known perfect localization results via Bessel function zeros.

Lower frequencies shift localization points and reduce localization quality, with complex return time dynamics.

Abstract

Intense AC electric fields on semiconductor structures have been studied in photon-assisted tunneling experiments with magnetic field applied either parallel (B_par) or perpendicular (B_per) to the interfaces. We examine here the electron dynamics in a double quantum well when intense AC electric fields F, and tilted magnetic fields are applied simultaneously. The problem is treated non-perturbatively by a time-dependent Hamiltonian in the effective mass approximation, and using a Floquet-Fourier formalism. For B_par=0, the quasi-energy spectra show two types of crossings: those related to different Landau levels, and those associated to dynamic localization (DL), where the electron is confined to one of the wells, despite the non-negligible tunneling between wells. B_par couples parallel and in-plane motions producing anti-crossings in the spectrum. However, since our approach is non-perturbative, we are able to explore the entire frequency range. For high frequencies, we reproduce the well known results of perfect DL given by zeroes of a Bessel function. We find also that the system exhibits DL at the same values of the field F, even as B_par non-zero, suggesting a hidden dynamical symmetry in the system which we identify with different parity operations. The return times for the electron at various values of field exhibit interesting and complex behavior which is also studied in detail. We find that smaller frequencies shifts the DL points to lower field F, and more importantly, yields poorer localization by the field. We analyze the explicit time evolution of the system, monitoring the elapsed time to return to a given well for each Landau level, and find non-monotonic behavior for decreasing frequencies.