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.

An 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 (10)

• The electronic properties of graphene
• Topological Insulators with Inversion Symmetry
• The Chiral Magnetic Effect
• 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
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Gravitational Anomaly and Transport
• Lorentz Invariance in Chiral Kinetic Theory
• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

Cited by in corpus (4)

• Anisotropic Fermi surface from holography
• Dilute magnetic topological semiconductors: What's new beyond the physics of dilute magnetic semiconductors?
• Anomalous Hall effects beyond Berry magnetic fields in a Weyl metal phase
• Interplay of the orbital magnetic moment and the chiral magnetic effect in Shubnikov-de Haas quantum oscillations