This article is cited in 8 papers

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

M. I. Katsnel'son^a, V. E. Nazaikinskii<sup>bcd

a</sup> 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.

Received: 19.03.2012

DOI: 10.4213/tmf8337

 English version: Theoretical and Mathematical Physics, 2012, 172:3, 1263–1277

Bibliographic databases:

• 
• 
• 
• 
• 
•