Modern theory of magnetic breakdown

Abstract

The modern semiclassical theory of a Bloch electron in a magnetic field encompasses the orbital magnetization and geometric phase. Beyond this semiclassical theory lies the quantum description of field-induced tunneling between semiclassical orbits, known as magnetic breakdown. Here, we synthesize the modern semiclassical notions with quantum tunneling -- into a single Bohr-Sommerfeld quantization rule that is predictive of magnetic energy levels. This rule is applicable to a host of topological solids with \emph{unremovable} geometric phase, that also \emph{unavoidably} undergo breakdown. A notion of topological invariants is formulated that nonperturbatively encode tunneling, and is measurable in the de-Haas-van-Alphen effect. Case studies are discussed for topological metals near a metal-insulator transition and over-tilted Weyl fermions.

5 pages, 2 figures

References in corpus (6)

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• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Computing topological invariants without inversion symmetry
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators
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Cited by in corpus (12)

• Quantum Transport in Topological Semimetals under Magnetic Fields
• Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet
• Theory of Difference Frequency Quantum Oscillations
• de Haas-van Alphen spectroscopy and fractional quantization of magnetic-breakdown orbits in moiré graphene
• High Landau levels of 2D electrons near the topological transition caused by interplay of spin-orbit and Zeeman energy shifts
• Quantum oscillation beyond the quantum limit in pseudospin Dirac materials
• Resonant contributions to oscillatory phenomena under conditions of magnetic breakdown during reconstructions of electron dynamics on the Fermi surface
• Is it possible to determine unambiguously the Berry phase solely from quantum oscillations?
• Scalable Sondheimer oscillations driven by commensurability between two quantizations
• A Fermi Surface Descriptor Quantifying the Correlations between Anomalous Hall Effect and Fermi Surface Geometry
• Dynamical magnetic breakdown and quantum oscillations from hot spot scattering
• On Fractional Quantum Hall Effect (FQHE): A Chern-Simons and nonequilibrium quantum transport Weyl transform approach