Exotic Lifshitz transitions in topological materials
G.E. Volovik a, b, c
a Low Temperature Laboratory, Aalto University, PO Box 15100, Aalto, FI-00076, Finland
b Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation
c Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
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.