What is it about?
We explore non-trivial geometric and topological issues associated with complex electronic spectra in conductors. The study of such issues is carried out by observing various electronic phenomena in strong magnetic fields. A number of deep mathematical theorems make it possible to connect the picture of observed phenomena with many important characteristics of electronic spectra in a wide variety of substances. The presented results are based mainly on the study of the topology of the system, which describes the dynamics of electrons in a crystal in the presence of external fields. Among the most important phenomena under study, transport and resonance electronic phenomena in strong magnetic fields can be especially highlighted.
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Why is it important?
The study of electronic spectra in crystals plays a very important role, since the shape of such spectra affects almost all phenomena occurring in them. Such studies are becoming especially important nowadays, due to the emergence of more and more new substances with very non-trivial electronic properties. The emergence of a wide variety of such substances gives hope for solving many problems that have been facing modern science for quite a long time (such problems include, in particular, the problem of the room temperature superconductivity and other important problems). The availability of serious mathematical methods for studying the electronic properties of such substances is very relevant in this situation.
Perspectives
Modern technologies provide enormous opportunities for applying the methods described in the work to a huge number of new substances. Such opportunities are due, in particular, to new methods of creating strong magnetic fields, obtaining ultra-pure single-crystal materials, achieving ultra-low temperatures, as well as a number of other achievements obtained recently. In this situation, the use of deep mathematical methods provides great prospects for the development of new approaches to the study of new substances and phenomena.
Andrey Maltsev
Read the Original
This page is a summary of: Topology of dynamical systems on the Fermi surface and galvanomagnetic phenomena in normal metals, Journal of Mathematical Physics, July 2024, American Institute of Physics,
DOI: 10.1063/5.0151512.
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