Modern semiclassical theory of magnetic transport and breakdown

Abstract

The Bohr-Sommerfeld quantization rule lies at the heart of the modern semiclassical theory of a Bloch electron in a magnetic field. This rule is predictive of Landau levels and quantum oscillations for conventional metals, as well as for a host of topological metals which have emerged in the recent intercourse between band theory, crystalline symmetries and topology. The essential ingredients in any quantization rule are connection formulae that match the semiclassical (WKB) wavefunction across regions of strong quantum fluctuations. Here, we propose (a) a multi-component WKB wavefunction that describes transport within degenerate-band subspaces, and (b) the requisite connection formulae for saddlepoints and type-II Dirac points, where tunneling respectively occurs within the same band, and between distinct bands. (a-b) extend previous works by incorporating phase corrections that are subleading in powers of the field; these corrections include the geometric Berry phase, and account for the orbital magnetic moment and the Zeeman coupling. A comprehensive symmetry analysis is performed for such phase corrections occurring in closed orbits, which is applicable to solids in any (magnetic) space group. We have further formulated a graph-theoretic description of semiclassical orbits. This allows us to systematize the construction of quantization rules for a large class of closed orbits (with or without tunneling), as well as to formulate the notion of a topological invariant in semiclassical magnetotransport -- as a quantity that is invariant under continuous deformations of the graph. Landau levels in the presence of tunneling are generically quasirandom, i.e., disordered on the scale of nearest-neighbor level spacings but having longer-ranged correlations; we develop a perturbative theory to determine Landau levels in such quasirandom spectra.

Version 2 accepted in PRB. Improved derivation of multi-component WKB wavefunction. Minor typographic errors corrected. 115 pages, 12 figures

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• Landau quantization of nearly degenerate bands, and full symmetry classification of avoided Landau-level crossings
• Theory of Difference Frequency Quantum Oscillations
• Quantum oscillations in the zeroth Landau Level and the serpentine Landau fan
• Magnetic susceptibility of topological semimetals
• Superconductivity in PtPb${}_4$ with Possible Nontrivial Band Topology
• Strong anisotropy of electron-phonon interaction in NbP probed by magnetoacoustic quantum oscillations
• Emergent topological quantum orbits in the charge density wave phase of kagome metal CsV${}_3$Sb${}_5$
• Open Momentum Space Method for Hofstadter Butterfly and the Quantized Lorentz Susceptibility
• Bloch oscillations in the magnetoconductance of twisted bilayer graphene
• Spontaneous Gully Polarized Quantum Hall States in ABA Trilayer Graphene
• Quantum oscillations of the magnetic torque in the nodal-line Dirac semimetal ZrSiS
• Low-frequency Quantum Oscillations from Interactions in Layered Metals
• State selection in frustrated magnets
• High Landau levels of 2D electrons near the topological transition caused by interplay of spin-orbit and Zeeman energy shifts
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• Diagnosing Altermagnetic Phases through Quantum Oscillations
• Effective theories for quantum spin clusters: Geometric phases and state selection by singularity
• Gully quantum Hall ferromagnetism in biased trilayer graphene
• Order by singularity in Kitaev clusters
• Fermi surface of magnetic kagome compound GdV6Sn6 investigated using de Haas van Alphen Oscillations
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• Kagomé quantum oscillations in graphene superlattices
• Reconstructions of the electron dynamics in magnetic field and the geometry of complex Fermi surfaces
• Dimensionality-dependent type-II Weyl semimetal state in Mo${}_{0.25}$W${}_{0.75}$Te${}_2$
• Inhomogeneity identification by measuring magnetic quantum oscillations
• Electronic band structure from quasiparticle interference and Landau quantization in WTe${}_2$
• Temperature dependence of quantum oscillations from non-parabolic dispersions
• Floquet-Engineering Weyl Points and Linked Fermi Arcs from Straight Nodal Lines
• Films of rhombohedral graphite as two-dimensional topological semimetals
• Distinctive features of oscillatory phenomena in reconstructions of the topological structure of electron trajectories on complex Fermi surfaces
• Anomalous quantum oscillations from boson-mediated interband scattering
• Resonant contributions to oscillatory phenomena under conditions of magnetic breakdown during reconstructions of electron dynamics on the Fermi surface
• Anomalous Landau levels and quantum oscillation in rotation-invariant insulators
• Dynamical magnetic breakdown and quantum oscillations from hot spot scattering