Electron localization in linear chains of identical loop scatterers

TL;DR

This paper demonstrates that electron localization occurs generally in linear chains of identical quantum wire loops with equal arm lengths when subjected to magnetic fields or spin-orbit interactions, regardless of loop shape.

Contribution

It introduces a transfer matrix-based formalism to predict electron localization in quantum wire loop chains under magnetic and spin-orbit effects.

Findings

Electron localization is shown to be a generic phenomenon in such chains.

A transfer matrix criterion for localization is developed.

A formalism for integrating transmission probabilities over wave vectors is provided.

Abstract

We show that electron localization is generic in a linear chain of identical simple quantum wire loops with equal arm lengths in the presence of either a perpendicular magnetic field or the spin-orbit interaction, and has less to do with the shapes of the loops. We calculate the transfer matrices for a general simple loop scatterer in the presence of these effects. Based on the knowledge of the transfer matrices, we thus provide a criterion for the occurrence of the localization and present a simple formalism to integrate the transmission probability over the injection wave vector of electron.