Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction

TL;DR

This paper investigates how magnetic fields and spin-orbit interactions, specifically Rashba coupling, influence localization phenomena in quantum graphs, revealing conditions that enhance or destroy localization effects.

Contribution

It introduces a general technique for analyzing embedded quantum graphs with magnetic and spin-orbit effects and explores their impact on localization phenomena.

Findings

Magnetic fields induce extreme localization in the quantum graph.

Rashba spin-orbit interaction can destroy localization at generic parameter values.

Certain parameter combinations lead to infinitely degenerate eigenvalues.

Abstract

A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in the T3 shaped quantum graph. We show that this effect is destroyed at generic values of the Rashba constant. On the other hand, for certain combinations of the Rashba constant and the magnetic parameters another series of infinitely degenerate eigenvalues appears.