Department of Physics, University of Oslo, Oslo 0316, Norway
A. F. Ioffe Physico-Technical Institute of Russian Academy of Sciences, St. Petersburg 194021, Russia
S. G. Sharapov
Bogolyubov Institute for Theoretical Physics, National Academy of Science of Ukraine, Kiev 03143, Ukraine
Dipartimento di Fisica e Geologia, Universitá degli Studi di Perugia, Via Pascoli, 06123 Perugia, Italy
Received March 9, 2021, published online June 25, 2021
In this short review we pass through the milestones in the studies of the electronic topological transitions (ETT) and focus on some recent applications of the ideas worked out in their classical theory. These are: two-dimensional electron systems, de Haas–van Alphen effect, classification of ETT in multidimensional systems, superconductivity in systems close to ETT, thermoelectricity in heavy-fermion systems, where the cascades of topological changes of Fermi surface (FS) are generated by magnetic field. The history of studies of ETT is inextricably linked with Kharkov school of condensed matter physics, with such names as I. M. Lifshitz, V. G. Bar’yakhtar and many other. Among them is Moisey Isaakovich Kaganov, who contributed much in studies of the role of geometry and topology of FS in physical properties of the metals. Two of the authors (A. V. and Y. G.) had a honor and pleasure to work with M. I. Kaganov — Y. M. Blanter, M. I. Kaganov, A. V. Pantsulaya, and A. A. Varlamov, Phys. Rep.245, 159 (1994) ; all of us have been learning the niceties of science from his books. “The Fermi surface is the stage on which the drama of the life of the electron is played out” wrote Kaganov and Lifshitz. We devote this work to their memory.
Key words: electronic topological transitions, two-dimensional electron systems, de Haas–van Alphen effect, superconductivity.