Beijing-Moscow Mathematics Colloquium (online)
Abstract
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 π-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 introduced by Atiyah, Patodi, and Singer and already having well-known applications (such as the Kopnin forces in superconductors and superfluids) in condensed matter physics.
Bio
Vladimir Nazaikinskii received PhD degree from Moscow Institute of Electronic Engineering in 1981 and DSc degree from Steklov Mathematical Institute of RAS in 2014 and was elected Corresponding Member of RAS in 2016. He works at Ishlinsky Institue for Problems in Mechanics of RAS as a principal researcher. His research interests include asymptotic methods in the theory of differential equations and mathematical physics; asymptotic methods in the statistics of many-particle systems and relations to number theory; C*-algebras and noncommutative geometry; elliptic theory and index theory.
