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Abstract
Topological Lifshitz transitions involve many types of topological structures in momentum and frequencymomentum spaces, such as Fermi surfaces, Dirac lines, Dirac and Weyl points, etc., each of which has its own stabilitysupporting topological invariant (N_{1}, N_{2}, N_{3}, N_{3}, etc.). The topology of the shape of Fermi surfaces and Dirac lines and the interconnection of objects of different dimensionalities produce a variety of Lifshitz transition classes. Lifshitz transitions have important implications for many areas of physics. To give examples, transitionrelated singularities can increase the superconducting transition temperature; Lifshitz transitions are the possible origin of the small masses of elementary particles in our Universe, and a black hole horizon serves as the surface of the Lifshitz transition between vacua with typeI and typeII Weyl points.
Original language  English 

Pages (fromto)  8998 
Number of pages  10 
Journal  PhysicsUspekhi 
Volume  61 
Issue number  1 
DOIs  
Publication status  Published  1 Jan 2018 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Black hole event horizon
 Dirac point
 Fermi surface
 Topological Lifshitz transitions
 Weyl point
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 1 Finished

TOPVAC: From Topological Matter to Relativistic Quantum Vacuum
Volovik, G. (Principal investigator), Nissinen, J. (Project Member), Eltsov, V. (Project Member), Rysti, J. (Project Member), Rantanen, R. (Project Member), Mäkinen, J. (Project Member), Zhang, K. (Project Member), Volard, M.M. (Project Member), Kamppinen, T. (Project Member) & Ikäheimo, A. (Project Member)
01/10/2016 → 30/09/2022
Project: EU: ERC grants