Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene

TL;DR

This paper explores the supersymmetry properties of Dirac vortex states in topological insulators and graphene, revealing analogies to the hydrogen atom's Runge-Lenz-Pauli vector and analyzing symmetry breaking effects.

Contribution

It extends the understanding of vortex Hamiltonian supersymmetry, highlighting its analogies to classical systems and examining how symmetry breaking influences degeneracy.

Findings

Supersymmetry of the vortex Hamiltonian is characterized and related to the Runge-Lenz-Pauli vector.

Residual degeneracy persists only when chemical potential and Zeeman field are equal in magnitude.

Symmetry breaking removes degeneracy unless specific conditions are met.

Abstract

The Dirac mass-vortex at the surface of a topological insulator or in graphene is considered. Within the linear approximation for the vortex amplitude's radial dependence, the spectrum is a series of degenerate bound states, which can be classified by a set of accidental SU(2) and supersymmetry generators (I. F. Herbut and C.-K. Lu, Phys. Rev. B 83 125412 (2011)). Here we discuss further the properties and manifestations of the supersymmetry of the vortex Hamiltonian, and point out some interesting analogies to the Runge-Lenz-Pauli vector in the non-relativistic hydrogen atom. Symmetry breaking effects due to a finite chemical potential, and the Zeeman field are also analyzed. We find that a residual accidental degeneracy remains only in the special case of equal magnitudes of both terms, whereas otherwise it becomes removed entirely.