Anomalous transport phenomena in Weyl metal beyond the Drude model for Landau's Fermi liquids

Abstract

Landau's Fermi-liquid theory is the standard model for metals, characterized by the existence of electron quasiparticles near a Fermi surface as long as Landau's interaction parameters lie below critical values for instabilities. Recently, this fundamental paradigm has been challenged by physics of strong spin-orbit coupling although the concept of electron quasiparticles remains valid near the Fermi surface, where the Landau's Fermi-liquid theory fails to describe electromagnetic properties of this novel metallic state, referred to as Weyl metal. A novel ingredient is that such a Fermi surface encloses a Weyl point with definite chirality, referred to as a chiral Fermi surface, which can arise from breaking of either time reversal or inversion symmetry in systems with strong spin-orbit coupling, responsible for both Berry curvature and chiral anomaly. As a result, electromagnetic properties of the Weyl metallic state are described not by conventional Maxwell equations but by axion electrodynamics, where Maxwell equations are modified with a topological-in-origin spatially modulated $\theta (\mathbf{r})\mathbf{E}\cdot \mathbf{B}$ term. This novel metallic state has been realized recently in Bi${}_{1-x}$Sb${}_x$ around $x\sim 3$ under magnetic fields, where the Dirac spectrum appears around the critical point between the normal semiconducting ($x<3$) and topological semiconducting phases ($x>3$) and the time reversal symmetry breaking perturbation causes the Dirac point to split into a pair of Weyl points along the direction of the applied magnetic field for such a strong spin-orbit coupled system. In this review article, we discuss how the topological structure of both the Berry curvature and chiral anomaly (axion electrodynamics) gives rise to anomalous transport phenomena in Bi${}_{1-x}$Sb${}_x$ around $x\sim 3$ under magnetic fields, modifying the Drude model of Landau's Fermi liquids.

arXiv commentAn invited review article for the STAM (Science and Technology of Advanced Materials (ISSN 1468-6996)) Focus issue "Materials Science of Topological Insulators and Superconductors"

References in corpus (24)

• The electronic properties of graphene
• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Topological Insulators with Inversion Symmetry
• Weyl Semimetal in a Topological Insulator Multilayer
• The Chiral Magnetic Effect
• Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological response in Weyl semimetals and the chiral anomaly
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Recent developments in transport phenomena in Weyl semimetals
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Gravitational Anomaly and Transport
• Chiral Kinetic Theory
• Axionic field theory of (3+1)-dimensional Weyl semi-metals
• Singular Fermi Liquids
• Berry curvature and 4-dimensional monopole in relativistic chiral kinetic equation
• Lorentz Invariance in Chiral Kinetic Theory
• Axion response in Weyl semimetals
• Triangle anomaly in Weyl semi-metals
• Boltzmann-equation approach to anomalous transport in a Weyl metal
• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
• Anomalous Chiral Fermi Surface

Cited by in corpus (14)

• Nernst and magneto-thermal conductivity in a lattice model of Weyl fermions
• Anisotropic Fermi surface from holography
• Dilute magnetic topological semiconductors: What's new beyond the physics of dilute magnetic semiconductors?
• A topological Fermi-liquid theory for interacting Weyl metals with time reversal symmetry breaking
• Chiral Waves on the Fermi-Dirac Sea: Quantum Superfluidity and the Axial Anomaly
• Chiral pair of Fermi arcs, anomaly cancelation, and spin or valley Hall effects in inversion symmetry-broken Weyl metals
• Two-parameter scaling theory of the longitudinal magnetoconductivity in a Weyl metal phase: Chiral anomaly, weak disorder, and finite temperature
• Transmission/reflection coefficients and Faraday/Kerr rotations as a function of applied magnetic fields in spin-orbit coupled Dirac metals
• Anomalous Hall effects beyond Berry magnetic fields in a Weyl metal phase
• Emergence of Weyl metals driven by doped magnetic impurities in spin-orbit coupled semiconductors
• Interplay between disorder and inversion symmetry: Extreme enhancement of the mobility near the Weyl point in BiTeI
• Weyl systems: anomalous transport normally explained
• Collective dynamics of Fermi-surface fluctuations in an interacting Weyl metal phase
• Interplay of the orbital magnetic moment and the chiral magnetic effect in Shubnikov-de Haas quantum oscillations