  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.
