Zero-energy states of massive Dirac equation in magnetic fields

Details Zero-energy states of massive Dirac equation in magnetic fields Zero-energy states of massive Dirac equation in magnetic fields

2009-10-26

arxiv.org/abs/0910.4906v2

Physical Review B, vol. 81, 205429 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1103/PhysRevB.81.205429

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.

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