Mechanism of the Resonant Enhancement of Electron Drift in Nanometre Semiconductor Superlattices Subjected to Electric and Inclined Magnetic Fields

TL;DR

This paper investigates the mechanism behind resonant electron drift enhancement in semiconductor superlattices under combined electric and inclined magnetic fields, revealing non-chaotic processes and conditions where drift increases without stochastic webs.

Contribution

It clarifies that drift enhancement occurs through non-chaotic mechanisms, extends the theory to finite temperatures, and corrects previous analytic results, offering a comprehensive understanding of the phenomenon.

Findings

Resonant drift enhancement can occur without stochastic webs.

Chaos tends to suppress, not promote, drift enhancement.

Heating does not negate the drift enhancement mechanism.

Abstract

We address the increase of electron drift velocity that arises in semiconductor superlattices (SLs) subjected to constant electric and magnetic fields. It occurs if the magnetic field possesses nonzero components both along and perpendicular to the SL axis and the Bloch oscillations along the SL axis become resonant with cyclotron rotation in the transverse plane. It is a phenomenon of considerable interest, so that it is important to understand the underlying mechanism. In an earlier Letter (Phys. Rev. Lett. 114, 166802 (2015)) we showed that, contrary to a general belief that drift enhancement occurs through chaotic diffusion along a stochastic web (SW) within semiclassical collisionless dynamics, the phenomenon actually arises through a non-chaotic mechanism. In fact, any chaos that occurs tends to reduce the drift. We now provide fuller details, elucidating the mechanism in physical terms, and extending the investigation. In particular, we: (i) demonstrate that pronounced drift enhancement can still occur even in the complete absence of an SW; (ii) show that, where an SW does exist and its characteristic slow dynamics comes into play, it suppresses the drift enhancement even before strong chaos is manifested; (iii) generalize our theory for non-small temperature, showing that heating does not affect the enhancement mechanism and accounting for some earlier numerical observations; (iv) demonstrate that certain analytic results reported previously are incorrect; (v) provide an extended critical review of the subject and closely related issues; and (vi) discuss some challenging problems for the future.