Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?

TL;DR

This paper investigates how a 2D periodic potential under a magnetic field causes a transition in electron transport, linking quantum phenomena to classical chaos and band structure interactions.

Contribution

It reveals a novel quantum transport transition caused by classical chaos and avoided band crossing in a 2D electron system with anisotropic modulation.

Findings

Transition to transport along stronger modulation direction

Localization in weaker modulation direction

Connection to avoided band crossing and classical chaos

Abstract

We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossing due to classical chaos.