Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance

TL;DR

This paper provides exact analytical results on quantum interference and magnetoconductance for strongly localized electrons in magnetic fields, revealing how interference patterns depend on lattice structure and magnetic flux orientation.

Contribution

It derives closed-form expressions for tunneling probabilities and magnetoconductance in 2D and 3D lattices, advancing understanding of localization effects in magnetic fields.

Findings

Exact tunneling probabilities in 2D lattices

Analytic magnetoconductance as a function of flux

Orientation-dependent interference patterns in 3D

Abstract

We study quantum interference effects on the transition strength for strongly localized electrons hopping on 2D square and 3D cubic lattices in a magnetic field B. In 2D, we obtain closed-form expressions for the tunneling probability between two arbitrary sites by exactly summing the corresponding phase factors of all directed paths connecting them. An analytic expression for the magnetoconductance, as an explicit function of the magnetic flux, is derived. In the experimentally important 3D case, we show how the interference patterns and the small-B behavior of the magnetoconductance vary according to the orientation of B.