Geodesic
The~Aharonov--Bohm effect for massless Dirac fermions and the~spectral flow of Dirac-type operators with classical boundary conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 437-453

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In topological terms, we compute the spectral flow of an arbitrary family of self-adjoint Dirac-type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and terminal operators of the family are conjugate by an automorphism of the bundle in which the operators act. We use this result to study conditions for the existence of a nonzero spectral flow of a family of self-adjoint Dirac-type operators with local boundary conditions in a two-dimensional domain with a nontrivial topology and discuss possible physical realizations of a nonzero spectral flow.
Keywords: Aharonov–Bohm effect, topological insulator, self-adjoint Dirac operator, spectral flow, Atiyah–Singer index theorem, Atiyah–Bott index theorem, index locality principle.
Mots-clés : massless Dirac fermion, graphene 
@article{TMF_2012_172_3_a7,
     author = {M. I. Katsnel'son and V. E. Nazaikinskii},
     title = {The~Aharonov--Bohm effect for massless {Dirac} fermions and the~spectral flow of {Dirac-type} operators with classical boundary conditions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {437--453},
     publisher = {mathdoc},
     volume = {172},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a7/}
}
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M. I. Katsnel'son; V. E. Nazaikinskii. The~Aharonov--Bohm effect for massless Dirac fermions and the~spectral flow of Dirac-type operators with classical boundary conditions. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 3, pp. 437-453. http://geodesic.mathdoc.fr/item/TMF_2012_172_3_a7/