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arXiv · 1010.0728

Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension

Igor F. Herbut·Chi-Ken Lu
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Abstract

It is shown that the square of the Dirac Hamiltonian with the isotropic mass-hedgehog potential in d dimensions is the number operator of fictitious bosons and fermions over d quantum states. This result allows one to obtain the complete spectrum and degeneracies of the Dirac Hamiltonian with the hedgehog mass configuration in any dimension. The result pertains to low-energy states in the core of a general superconducting or insulating vortex in graphene in two dimensions, and in the superconducting vortex at the topological - trivial insulator interface in three dimensions, for example. The spectrum in d=2 is also understood in terms of the underlying accidental SU(2) symmetry and the supersymmetry of the Hamiltonian.

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Igor F. Herbut, Chi-Ken Lu. 2011-03-25. Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension. https://doi.org/10.1103/physrevb.83.125412

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