Topological Insulators Quantum Mechanics

TL;DR

This paper models three-dimensional topological insulators using supersymmetric quantum mechanics, revealing spin-orbit coupling as an emergent $SU(2)$ connection, and demonstrates the approach with examples like the harmonic oscillator and Aharonov-Bohm effect.

Contribution

It introduces a general supersymmetric quantum mechanics framework for topological insulators, linking spin-orbit coupling to $SU(2)$ connections and enabling standard quantum mechanical analysis.

Findings

Spin-orbit coupling arises from supersymmetrization.

The approach is applicable to any 3D quantum system.

Illustrated with harmonic oscillator and Aharonov-Bohm effect.

Abstract

Topological insulators in three dimensions are studied as a problem of supersymmetric quantum mechanics. The spin-orbit coupling is induced as a consequence of the supersymmetrization procedure and we show that it is equivalent to the appearance of a $SU(2)$ connection. The procedure presented in this letter is general and valid for any three-dimensional quantum system. The approach allows -- in principle -- to study a wide range of topological insulators as standard quantum mechanical problems. As an illustration the three-dimensional harmonic oscillator and the Aharonov-Bohm effect are studied in detail.