Topological insulators in relativistic quantum mechanics

Abstract

By employing supersymmetric quantum mechanics, the analog of relativistic quantum mechanics for topological insulators is considered. The procedure determines the general structure of the spin–orbit coupling even though it constrains the coupling constant. Through analogies with nonelativistic quantum mechanics, we construct relativistic Hamiltonians that share properties of topological insulators. As an application of our results, we study in detail the nonabelian extension of the Dirac–Landau oscillator and relativistic scattering with a spin–orbit coupling term.