Landaus Fermi-liquid theory is the standard model for metals, characterized by the existence of electron quasiparticles near a Fermi surface as long as Landaus interaction parameters lie below critical values for instabilities. Recently, this fundame
ntal 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 Landaus 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 $theta(bm{r}) bm{E} cdot bm{B}$ 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 Landaus Fermi liquids.
Weyl metal is regarded as a platform toward interacting topological states of matter, where its topological structure gives rise to anomalous transport phenomena, referred to as chiral magnetic effect and negative magneto-resistivity, the origin of w
hich is chiral anomaly. Recently, the negative magneto-resistivity has been observed with the signature of weak anti-localization at $x = 3 sim 4 ~ %$ in Bi$_{1-x}$Sb$_{x}$, where magnetic field is applied in parallel with electric field. Based on the Boltzmann-equation approach, we find the negative magneto-resistivity in the presence of weak anti-localization. An essential ingredient is to introduce the topological structure of chiral anomaly into the Boltzmann-equation approach, resorting to semi-classical equations of motion with Berry curvature.
Dirac metals (gapless semi-conductors) are believed to turn into Weyl metals when perturbations, which break either time reversal symmetry or inversion symmetry, are employed. However, no experimental evidence has been reported for the existence of W
eyl fermions in three dimensions. Applying magnetic fields near the topological phase transition from a topological insulator to a band insulator in Bi1-xSbx, we observe not only the weak anti-localization phenomenon in magnetoconductivity near zero magnetic fields (B < 0.4 T) but also its upturn above 0.4 T only for E // B. This incompatible coexistence between weak anti-localization and negative magnetoresistivity is attributed to the Adler-Bell-Jackiw anomaly (topological E B term) in the presence of weak anti-localization corrections.
We propose a phase diagram for FexBi2Te3 (0 < x < 0.1) single crystals, which belong to a class of magnetically bulk-doped topological insulators. The evolution of magnetic correlations from ferromagnetic- to antiferromagnetic- gives rise to topologi
cal phase transitions, where the paramagnetic topological insulator of Bi2Te3 turns into a band insulator with ferromagnetic-cluster glassy behaviours around x ~ 0.025, and it further evolves to a topological insulator with valence-bond glassy behaviours, which spans over the region between x ~ 0.03 up to x ~ 0.1. This phase diagram is verified by measuring magnetization, magnetotransport, and angle-resolved photoemission spectra with theoretical discussions.
Topological states of matter challenge the paradigm of symmetry breaking, characterized by gapless boundary modes and protected by the topological property of the ground state. Recently, angle-resolved photoemission spectroscopy (ARPES) has revealed
that semiconductors of Bi$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ belong to such a class of materials. Here, we present undisputable evidence for the existence of gapless surface Dirac fermions from transport in Bi$_{2}$Te$_{3}$. We observe Sondheimer oscillation in magnetoresistance (MR). This oscillation originates from the quantization of motion due to the confinement of electrons within the surface layer. Based on Sondheimers transport theory, we determine the thickness of the surface state from the oscillation data. In addition, we uncover the topological nature of the surface state, fitting consistently both the non-oscillatory part of MR and the Hall resistance. The side-jump contribution turns out to dominate around 1 T in Hall resistance while the Berry-curvature effect dominates in 3 T $sim$ 4 T.
