

Beijing–Moscow Mathematics Colloquium
January 15, 2021 12:00–13:00, Moscow, online






Partial spectral flow and the AharonovBohm effect in graphene
V. E. Nazaikinskii^{} ^{} Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow

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Abstract:
We study the AharonovBohm effect in an openended 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 tightbinding Hamiltonian of $\pi$electrons unavoidably cross the Fermi level, which results in the creation of electronhole 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 introduced by Atiyah, Patodi, and Singer and already having wellknown applications (such as the Kopnin forces in superconductors and superfluids) in condensed matter physics.
Language: English
Website:
https://zoom.com.cn/j/64523635960?pwd=dVo4eWdQeW90MThXd0NWZk1HdVBoUT09
^{*} Номер конференции в Zoom: 645 2363 5960 Пароль конференции: 714716

