Topo-fermiology

Abstract

The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase ($\lambda$) that is subleading in powers of the field; $\lambda$ is measurable in the phase offset of the de Haas-van Alphen oscillation, as well as of fixed-bias oscillations of the differential conductance in tunneling spectroscopy. In some solids and for certain field orientations, $\lambda /\pi$ are robustly integer-valued owing to the symmetry of the extremal orbit, i.e., they are the topological invariants of magnetotransport. Our comprehensive symmetry analysis identifies solids in any (magnetic) space group for which $\lambda$ is a topological invariant, as well as identifies the symmetry-enforced degeneracy of Landau levels. The analysis is simplified by our formulation of ten (and only ten) symmetry classes for closed, Fermi-surface orbits. Case studies are discussed for graphene, transition metal dichalchogenides, 3D Weyl and Dirac metals, and crystalline and ${\mathbb{Z}}_2$ topological insulators. In particular, we point out that a $\pi$ phase offset in the fundamental oscillation should \emph{not} be viewed as a smoking gun for a 3D Dirac metal.

Update: (i) Generalized Lifshitz-Kosevich formulae (for the oscillatory magnetization and density of states) which apply also in magnetic solids. (ii) Case studies on Bi2Se3 and Na3Bi. A $\pi$ phase offset in the fundamental oscillation should not be viewed as a smoking gun for a 3D Dirac metal. (iii) A zero-sum rule for $\lambda$ is derived for bulk orbits in time-reversal-symmetric metals

References in corpus (13)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Linear magnetoresistance caused by mobility fluctuations in the n-doped Cd3As2
• Phase analysis of quantum oscillations in graphite
• Topological-Metal to Band-Insulator Transition in (Bi1-xInx)2Se3 Thin Films
• Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators
• Bulk crystal growth and electronic characterization of the 3D Dirac Semimetal Na3Bi
• Probing the Fermi Surface of 3D Dirac Semimetal Cd${}_3$As${}_2$ through de Haas-van Alphen Technique
• Modern theory of magnetic breakdown
• Planar tunneling spectroscopy of the topological Kondo insulator SmB${}_6$

Cited by in corpus (34)

• Diagrammatic approach to nonlinear optical response with application to Weyl semimetals
• 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
• Topological Bloch oscillations
• Topological metals and finite-momentum superconductors
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Single crystal growth and magnetoresistivity study of topological semimetal CoSi
• Twisted Fermi surface of a thin-film Weyl semimetal
• Unusual magnetotransport in holmium monoantimonide
• Quantum Transport in Topological Semimetals under Magnetic Fields (II)
• Landau levels, response functions and magnetic oscillations from a generalized Onsager relation
• Quantum Oscillations in the Field-induced Ferromagnetic State of MnBi${}_{2-x}$Sb${}_x$Te${}_4$
• Bulk Fermi surface of the layered superconductor TaSe3 with three-dimensional strong topological insulator state
• Landau quantization of nearly degenerate bands, and full symmetry classification of avoided Landau-level crossings
• de Haas-van Alphen spectroscopy and fractional quantization of magnetic-breakdown orbits in moiré graphene
• Superconductivity in PtPb${}_4$ with Possible Nontrivial Band Topology
• Strong anisotropy of electron-phonon interaction in NbP probed by magnetoacoustic quantum oscillations
• Non-trivial quantum oscillation geometric phase shift in a trivial band
• Theory of shift current in Anderson insulator
• Real spin and pseudospin topologies in the noncentrosymmetric topological nodal-line semimetal CaAgAs
• 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 oscillations in 2D electron gases with spin-orbit and Zeeman interactions
• Charge order induced Dirac pockets in the nonsymmorphic crystal TaTe${}_4$
• Orbit topology analysed from $\pi$ phase shift of magnetic quantum oscillations in three-dimensional Dirac semimetal
• Fermi surface of magnetic kagome compound GdV6Sn6 investigated using de Haas van Alphen Oscillations
• Dimensionality-dependent type-II Weyl semimetal state in Mo${}_{0.25}$W${}_{0.75}$Te${}_2$
• Inhomogeneity identification by measuring magnetic quantum oscillations
• Temperature dependence of quantum oscillations from non-parabolic dispersions
• Phase of quantum oscillation in Weyl semimetals
• Anomalous quantum oscillations from boson-mediated interband scattering
• Fermi surface and Berry phase analysis for Dirac nodal line semimetals: cautionary tale to SrGa${}_2$ and BaGa${}_2$
• Evidence for strong electron correlations in a non-symmorphic Dirac semimetal