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TMF, 2012, Volume 172, Number 3, Pages 437–453 (Mi tmf8337)  

This article is cited in 3 scientific papers (total in 3 papers)

The Aharonov–Bohm effect for massless Dirac fermions and the spectral flow of Dirac-type operators with classical boundary conditions

M. I. Katsnel'sona, V. E. Nazaikinskiibcd

a Institute for Molecules and Materials, Radboud University Nijmegen, Nijmegen, The Netherlands
b Ishlinsky Institute for Problems in Mechanics, RAS, Moscow, Russia
c Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
d Moscow State Institute for Electronics and Mathematics, Moscow, Russia

Abstract: 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, massless Dirac fermion, graphene, topological insulator, self-adjoint Dirac operator, spectral flow, Atiyah–Singer index theorem, Atiyah–Bott index theorem, index locality principle

DOI: https://doi.org/10.4213/tmf8337

Full text: PDF file (652 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 172:3, 1263–1277

Bibliographic databases:

Document Type: Article
Received: 19.03.2012

Citation: 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”, TMF, 172:3 (2012), 437–453; Theoret. and Math. Phys., 172:3 (2012), 1263–1277

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Prokhorova M., “The Spectral Flow for Dirac Operators on Compact Planar Domains with Local Boundary Conditions”, Commun. Math. Phys., 322:2 (2013), 385–414  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Tudorovskiy T., Nazaikinskii V.E., Katsnelson M.I., “Spectral Flow for Aharonov-Bohm Rings Generated by Zero-MASS Lines”, Phys. Status Solidi-Rapid Res. Lett., 7:1-2, SI (2013), 157–159  crossref  adsnasa  isi  elib
    3. [Anonymous], “The Maslov Index in Symplectic Banach Spaces”, Mem. Am. Math. Soc., 252:1201 (2018), 1+  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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