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

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.

revised version with added reference and a new paragraph on interpretation of two-velocity Weyl fermions realized in 2D optical lattice; to appear in J Phys A

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• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Electron fractionalization in two-dimensional graphenelike structures
• Chiral Gauge Theory for Graphene
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