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

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.

6 pages: typos corrected, new section on accidental supersymmetry, added references, many comments, and a figure. Published version

References in corpus (11)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Electron fractionalization in two-dimensional graphenelike structures
• Theory of interacting electrons on the honeycomb lattice
• Chiral Gauge Theory for Graphene
• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• Persistence of zero modes in a gauged Dirac model for bilayer graphene
• Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene
• Midgap spectrum of the fermion-vortex system
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Cited by in corpus (10)

• Strain-induced time-reversal odd superconductivity in graphene
• Isospin of topological defects in Dirac systems
• Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions
• Ettingshausen effect due to Majorana modes
• Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene
• Zero modes of the generalized fermion-vortex system in magnetic field
• Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order
• Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions
• Quantum Mechanical Hamiltonians with Large Ground-State Degeneracy
• Spectrum of the Vortex Bound States of the Dirac and Schrodinger Hamiltonian in the presence of Superconducting Gaps