Regular Article – Theoretical Physics
Partial spectral flow and the Aharonov–Bohm effect in graphene
Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525AJ, Nijmegen, The Netherlands
2 Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Vernadsky Ave., 119526, Moscow, Russia
3 Moscow Institute of Physics and Technology, Institutsky Lane 9, 141700, Dolgoprudny, Moscow Region, Russia
Accepted: 10 September 2020
Published online: 25 September 2020
We study the Aharonov–Bohm effect in an open-ended tube made of a graphene sheet whose dimensions are much larger than the interatomic distance in graphene. An external magnetic field vanishes on and in the vicinity of the graphene sheet and its flux through the tube is adiabatically switched on. It is shown that, in the process, the energy levels of the tight-binding Hamiltonian of -electrons unavoidably cross the Fermi level, which results in the creation of electron–hole pairs. The number of pairs is proven to be equal to the number of magnetic flux quanta of the external field. The proof is based on the new notion of partial spectral flow, which generalizes the ordinary spectral flow already having well-known applications (such as the Kopnin forces in superconductors and superfluids) in condensed matter physics.
© The Author(s) 2020
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