Topological Lifshitz transitions involve many types of topological structures in momentum and frequency-momentum spaces, such as Fermi surfaces, Dirac lines, Dirac and Weyl points, etc., each of which has its own stability-supporting topological invariant (N₁, N₂, N₃, Ñ₃, etc.). The Fermi surface and Dirac line topologies and the interconnection of objects of different dimensionality produce a variety of Lifshitz transition classes. Lifshitz transitions have important implications for many areas of physics. To give examples, transition-related singularities can increase the superconducting transition temperature; Lifshitz transitions are the possible origin of the small masses of elementary particles in our Universe; a black hole horizon serves as the surface of Lifshitz transition between the vacua with type-I and type-II Weyl points, etc.

Keywords: topological Lifshitz transitions, Fermi surface, Dirac point, Weyl point, black hole event horizon PACS: 04.70.−s, 71.30.+h, 73.22.−f (all) DOI: 10.3367/UFNe.2017.01.038218 URL: https://ufn.ru/en/articles/2018/1/g/ 000429883000005 2-s2.0-85045746660 2018PhyU...61...89V Citation: Volovik G E "Exotic Lifshitz transitions in topological materials" Phys. Usp. 61 89–98 (2018) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 23rd, January 2017, accepted: 18th, January 2017 Оригинал: Воловик Г Е «Экзотические переходы Лифшица в топологической материи» УФН 188 95–105 (2018); DOI: 10.3367/UFNr.2017.01.038218