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Review Article
Open Access
Fermiology of Topological Metals
- A. Alexandradinata1, and Leonid Glazman2
- Vol. 14:261-309 (Volume publication date March 2023) https://doi.org/10.1146/annurev-conmatphys-040721-021331
- First published as a Review in Advance on December 08, 2022
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Copyright © 2023 by the author(s).This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See credit lines of images or other third-party material in this article for license information
Abstract
The modern scope of fermiology encompasses not just the classical geometry of Fermi surfaces but also the geometry of quantum wave functions over the Fermi surface. This enlarged scope is motivated by the advent of topological metals—metals whose Fermi surfaces are characterized by a robustly nontrivial Berry phase. We review the extent to which topological metals can be diagnosed from magnetic-field-induced quantum oscillations of transport and thermodynamic quantities. A holistic analysis of the oscillatory wave form is proposed, in which different characteristics of the wave form (e.g., phase offset, high-harmonic amplitudes, temperature-dependent frequency) encode different aspects of a topologically nontrivial Fermi surface. Which characteristic to focus on depends on (a) the orientation of the magnetic field relative to certain crystallographic axes, (b) the symmetry class of the topological metal, and (c) the separation of Fermi-surface pockets in quasimomentum space. Closely proximate pockets arise when (1) spin–split pockets are nearly overlapping due to a weak spin–orbit force or when (2) two pockets touch at an isolated point, which can be a topological band-touching point or a saddlepoint in the energy-momentum dispersion. The emergence of a pseudospin degree of freedom (in case 1) and the implications of magnetic breakdown (in case 2) are reviewed, with emphasis on new aspects originating from the (nonabelian) Berry connection of the Fermi surface. Future extensions of topofermiology are suggested in the directions of interaction-induced Fermi-liquid instabilities and two-dimensional electron liquids.
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