Aharonov-Bohm cages in two-dimensional structures

TL;DR

This paper explores a magnetic-field-induced localization mechanism in two-dimensional structures, introducing Aharonov-Bohm cages that confine electron wavepackets and lead to unique quantum dynamics across various tilings.

Contribution

It introduces the concept of Aharonov-Bohm cages as a new localization phenomenon applicable to diverse two-dimensional tilings.

Findings

Localization occurs at specific magnetic flux values.

Wavepackets are confined within Aharonov-Bohm cages.

Quantum dynamics show pulsating behavior.

Abstract

We present an extreme localization mechanism induced by a magnetic field for tight-binding electrons in two-dimensional structures. This spectacular phenomenon is investigated for a large class of tilings (periodic, quasiperiodic, or random). We are led to introduce the Aharonov-Bohm cages defined as the set of sites eventually visited by a wavepacket that can, for particular values of the magnetic flux, be bounded. We finally discuss the quantum dynamics which exhibits an original pulsating behaviour.