Zero-energy states of massive Dirac equation in magnetic fields

Abstract

The Dirac equation with a U(1) vortex in the mass-term is solved in the presence of magnetic-like fields at zero energy. By drawing an analogy to classical mechanics, it is shown that the four-component Dirac equation in arbitrary magnetic field always yields one zero-energy state. In the time-reversal preserving, pseudo-magnetic field, however, the number of zero-energy states may depend on the field's profile and sign. Some explicit examples are worked out. Possible implications of these results for the charge of the vortex and for the behavior of graphene in magnetic field are discussed.

5 revtex pages; cosmetic changes, updated references, published version

References in corpus (15)

• Strong suppression of weak (anti)localization in graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Theory of interacting electrons on the honeycomb lattice
• Chiral Gauge Theory for Graphene
• Theory of integer quantum Hall effect in graphene
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• Field-induced Kosterlitz-Thouless transition in the N=0 Landau level of graphene
• Electron fractionalization for two-dimensional Dirac fermions
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
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• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice

Cited by in corpus (18)

• Vortices and Other Topological Solitons in Dense Quark Matter
• Isospin of topological defects in Dirac systems
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Asymmetric spatial structure of zero modes for birefringent Dirac fermions
• Magnetic field induced inequivalent vortex zero modes in strained graphene
• Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension
• Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene
• Majorana zero modes bound to a vortex line in a topological superconductor
• Pairing symmetry and vortex zero-mode for superconducting Dirac fermions
• Z${}_2$ index theorem for Majorana zero modes in a class D topological superconductor
• $Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions
• Chiral condensate with topological degeneracy in graphene and its manifestation in edge states
• Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene
• Conserved charges of order-parameter textures in Dirac systems
• Zero modes of the generalized fermion-vortex system in magnetic field
• Induced fractional valley number in graphene with topological defects
• Spin-resoloved chiral condensate as a spin-unpolarized ν=0 quantum Hall state in graphene
• Zero modes and index theorems for non-Hermitian Dirac fermions