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Register a new userNonlocal transport phenomena in Weyl metals beyond the mesoscopic scale
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Axion electrodynamics governs electromagnetic properties of Weyl metals. Although transmission and reflection measurements of light have been proposed to confirm the axion electrodynamics, there are still lack of theoretical proposals for macroscopic nonlocal transport phenomena in Weyl metals. In this paper, we present nonlocal transport phenomena in time reversal symmetry-broken (TRSB) Weyl metals. Solving the axion electrodynamics numerically, we show that such nonlocal transport phenomena arise from the negative longitudinal magneto-resistivity (NLMR), combined with the anomalous Hall effect (AHE) in the axion electrodynamics. Since this nonlocal transport occurs beyond the mesoscopic scale, we conclude that these nonlocal properties have nothing to do with Fermi arcs, regarded to be clear evidence of the axion electrodynamics in the bulk.
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Recently synthesized 3D materials with Dirac spectrum exhibit peculiar electric transport qualitatively different from its 2D analogue, graphene. Neglecting impuritiy scattering, the real part of the conductivity is strongly frequency dependent (linear), while the imaginary part is non-zero (unlike in undoped, clean graphene). The Coulomb interaction between electrons is unscreened as in a dielectric and hence is long range. We demonstrate that the interaction correction renders the electrodynamics nonlocal on a mesoscopic scale. The longitudinal conductivity $sigma _{L}$ (related by charge conservation to the electric susceptibility) and the transverse conductivity $sigma _{T}$ are different in the long wave length limit and consequently the standard local Ohms law description does not apply. This leads to several remarkable effects in transport and optical response. We predict a charging effect in DC transport that is a direct signature of the nonlocality. The optical response of the WSM is also sensitive to the nonlocality. In these materials p-polarized light generates bulk plasmons as well as the transversal waves. The propagation inside the WSM is only slightly attenuated. At a specific (material parameter dependent) frequency the two modes coincide, a phenomenon impossible in a local medium. Remarkably, for any frequency there is an incident angle where total absorption occurs, turning the WSM opaque.
We report on a study of intrinsic superconductivity in a Weyl metal, i.e. a doped Weyl semimetal. Two distinct superconducting states are possible in this system in principle: a zero-momentum pairing BCS state, with point nodes in the gap function; and a finite-momentum FFLO-like state, with a full nodeless gap. We find that, in an inversion-symmetric Weyl metal the odd-parity BCS state has a lower energy than the FFLO state, despite the nodes in the gap. The FFLO state, on the other hand, may have a lower energy in a noncentrosymmetric Weyl metal, in which Weyl nodes of opposite chirality have different energy. However, realizing the FFLO state is in general very difficult since the paired states are not related by any exact symmetry, which precludes a weak-coupling superconducting instability. We also discuss some of the physical properties of the nodal BCS state, in particular Majorana and Fermi arc surface states.
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 Weyl 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.
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 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 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.
The dynamo effect is a class of macroscopic phenomena responsible for generation and maintaining magnetic fields in astrophysical bodies. It hinges on hydrodynamic three-dimensional motion of conducting gases and plasmas that achieve high hydrodynamic and/or magnetic Reynolds numbers due to large length scales involved. The existing laboratory experiments modeling dynamos are challenging and involve large apparatuses containing conducting fluids subject to fast helical flows. Here we propose that electronic solid-state materials -- in particular, hydrodynamic metals -- may serve as an alternative platform to observe some aspects of the dynamo effect. Motivated by recent experimental developments, this paper focuses on hydrodynamic Weyl semimetals, where the dominant scattering mechanism is due to interactions. We derive Navier-Stokes equations along with equations of magneto-hydrodynamics that describe transport of Weyl electron-hole plasma appropriate in this regime. We estimate the hydrodynamic and magnetic Reynolds numbers for this system. The latter is a key figure of merit of the dynamo mechanism. We show that it can be relatively large to enable observation of the dynamo-induced magnetic field bootstrap in experiment. Finally, we generalize the simplest dynamo instability model -- Ponomarenko dynamo -- to the case of a hydrodynamic Weyl semimetal and show that the chiral anomaly term reduces the threshold magnetic Reynolds number for the dynamo instability.
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