Topological Insulators Quantum Mechanics

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.

Relativistic Topological Insulator Model

“…In 2 + 1-dimensions this procedure was also studied by Benevig and Zhang who explicitly showed how a topological insulator mimics as two Landau problems with opposite magnetic fields thus providing the Z 2 -symmetry [5]. Under these conditions it seems natural to ask how this viewpoint works in the relativistic domain and how these ideas could provide a new approach to problems in high energy physics and mathematical physics [6].…”