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.

arXiv comment5 pages, 2 figures

References in corpus (22)

• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Type-II Weyl Semimetals
• Experimental discovery of Weyl semimetal TaAs
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
• Computing topological invariants without inversion symmetry
• Landau Quantization and Quasiparticle Interference in the Three-Dimensional Dirac Semimetal Cd3As2
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids
• Magnetic breakdown and Klein tunneling in a type-II Weyl semimetal
• Wannier Center Sheets in Topological Insulators
• Topological Insulators from Group Cohomology
• Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators
• Symmetry breaking and Landau quantization in topological crystalline insulators
• De Haas-van Alphen effect in two- and quasi two-dimensional metals and superconductors
• Berry-phase description of Topological Crystalline Insulators
• Topology and Interactions in a Frustrated Slab: Tuning from Weyl Semimetals to C > 1 Fractional Chern Insulators
• Coulomb interaction effect in tilted Weyl fermion in two dimensions
• Cyclotron resonance of figure-of-eight orbits in a type-II Weyl semimetal

Cited by in corpus (31)

• Quantum Transport in Topological Semimetals under Magnetic Fields
• Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-line Semimetals
• Modern semiclassical theory of magnetic transport and breakdown
• Topo-fermiology
• Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet
• Electron-hole tunneling revealed by quantum oscillations in the nodal-line semimetal HfSiS
• Twisted Fermi surface of a thin-film Weyl semimetal
• Topological and trivial magnetic oscillations in nodal loop semimetals
• Quantum Transport in Topological Semimetals under Magnetic Fields (II)
• Quantum oscillations probe the Fermi surface topology of the nodal-line semimetal CaAgAs
• 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
• de Haas-van Alphen spectroscopy and fractional quantization of magnetic-breakdown orbits in moiré graphene
• Low-frequency Quantum Oscillations from Interactions in Layered Metals
• High Landau levels of 2D electrons near the topological transition caused by interplay of spin-orbit and Zeeman energy shifts
• Phase shift of cyclotron orbits at type-I and type-II multi-Weyl nodes
• Quantum oscillation beyond the quantum limit in pseudospin Dirac materials
• Type-II Dirac line node in strained Na3N
• Spinful Aubry-Andre model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling
• Semiclassical transport with Berry curvature: Chambers formula and applications to systems with Fermi surface topological transitions
• Magnetic breakdown spectrum of a Kramers-Weyl semimetal
• Dimensionality-dependent type-II Weyl semimetal state in Mo${}_{0.25}$W${}_{0.75}$Te${}_2$
• Scalable Sondheimer oscillations driven by commensurability between two quantizations
• Resonant contributions to oscillatory phenomena under conditions of magnetic breakdown during reconstructions of electron dynamics on the Fermi surface
• Spin mixing between subbands and extraordinary Landau levels shift in wide HgTe quantum wells
• Is it possible to determine unambiguously the Berry phase solely from quantum oscillations?
• On Fractional Quantum Hall Effect (FQHE): A Chern-Simons and nonequilibrium quantum transport Weyl transform approach
• 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