Concise guide for electronic topological transitions

Abstract

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 "Musik", as all friends called Kaganov; 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.

arXiv comment13 pages, 9 figures, any comments are welcome

References in corpus (17)

• Critical change in the Fermi surface of iron arsenic superconductors at the onset of superconductivity
• Iron based superconductors: magnetism, superconductivity and electronic structure
• Resonant and crossover phenomena in a multiband superconductor tuning the chemical potential near a band edge
• Importance of Fermi surface topology for high temperature superconductivity in electron-doped iron arsenic superconductors
• Topological Lifshitz transitions
• Exotic Lifshitz transitions in topological materials
• Superconductivity in an electron band just above the Fermi level: possible route to BCS-BEC superconductivity
• Direct Observation of a Uniaxial Stress-driven Lifshitz Transition in Sr${}_2$RuO${}_4$
• Observation of strong electron pairing on bands without Fermi surfaces in LiFe1-xCoxAs
• Anomalous isotope effect near a 2.5 Lifshitz transition in a multi-band multi-condensate superconductor made of a superlattice of stripes
• A key role of correlation effects in the Lifshitz transition in Sr${}_2$RuO${}_4$
• Shape resonance for the anisotropic superconducting gaps near a Lifshitz transition: the effect of electron hopping between layers
• Strongly correlated two-dimensional plasma explored from entropy measurements
• Cascade of magnetic field induced Lifshitz transitions in the ferromagnetic Kondo lattice material YbNi4P2
• Quantization of entropy in a quasi-two-dimensional electron gas
• Anomalous density of states in multiband superconductors near Lifshitz transition
• Transport Spectroscopy of the Field Induced Cascade of Lifshitz Transitions in YbRh2Si2

Cited by in corpus (9)

• Field-Induced Lifshitz Transition in the Magnetic Weyl Semimetal Candidate PrAlSi
• The Lifshitz nature of the transition between the gap and gapless states of a superconductor
• Topological nature of the transition between the gap and the gapless superconducting states
• Tunable chiral anomalies and coherent transport on a honeycomb lattice
• Density of states and differential entropy in Dirac materials in crossed magnetic and in-plane electric fields
• Negatively enhanced thermopower near a Van Hove singularity in electron-doped Sr${}_2$RuO${}_4$
• Pressure induced superconducting dome in LaNiGa2
• Pressure-induced exciton formation and superconductivity in platinum-based mineral Sperrylite
• Universal transport at Lifshitz metal-insulator transitions in two dimensions