Chiral kinetic theory

Effective Chiral Magnetic Effect from Neutrino Radiation

We develop an approach to chiral kinetic theories for electrons close to equilibrium and neutrinos away from equilibrium based on a systematic power counting scheme for different timescales of electromagnetic and weak interactions. Under this framework, we derive electric and energy currents along magnetic fields induced by neutrino radiation in general nonequilibrium states. This may be regarded as an effective chiral magnetic effect (CME), which is present without a chiral chemical potential, unlike the conventional CME. We also consider the so-called gain region of core-collapse supernovae as an example and find that the effective CME enhanced by persistent neutrino emission in time is sufficiently large to lead to the inverse cascade of magnetic and fluid kinetic energies and observed magnitudes of pulsar kicks. Our framework may also be applicable to other dense-matter systems involving nonequilibrium neutrinos.

Constraining Non-Dissipative Transport Coefficients in Global Equilibrium

The fluid in global equilibrium must fulfill some constraints. These constraints can be derived from quantum statistical theory or kinetic theory. In this work, we show how these constraints can be applied to determine the non-dissipative transport coefficients for chiral systems along with the energy-momentum conservation, chiral anomaly for charge current and trace anomaly in the energy-momentum tensor.

Anomalous Electromagnetic Field Penetration in a Weyl or Dirac Semimetal

The current response to an electromagnetic field in a Weyl or Dirac semimetal becomes nonlocal due to the chiral anomaly activated by an applied static magnetic field. The nonlocality develops under the conditions of the normal skin effect and is related to the valley charge imbalance generated by the joint effect of the electric field of the impinging wave and the static magnetic field. We elucidate the signatures of this nonlocality in the transmission of electromagnetic waves. The signatures include enhancement of the transmission amplitude and its specific dependence on the wave's frequency and the static magnetic field strength.

Skin effect as a probe of transport regimes in Weyl semimetals

Weyl semimetals are a class of three-dimensional materials, whose low-energy excitations mimic massless fermions. In consequence they exhibit various unusual transport properties related to the presence of chiral anomalies, a subtle quantum phenomenon that denotes the breaking of the classical chiral symmetry by quantum fluctuations. In this work we present a universal description of transport in weakly disordered Weyl semimetals with several scattering mechanisms taken into account. Our work predicts the existence of a new anomaly-induced transport regime in these materials and gives a crisp experimental signature of a chiral anomaly in optical conductivity measurements. Finally, by also capturing the hydrodynamic regime of quasiparticles, our construction bridges the gap between developments in electronic fluid mechanics and three-dimensional semimetals.

We study the propagation of an oscillatory electromagnetic field inside a Weyl semimetal. In conventional conductors, the motion of the charge carriers in the skin layer near the surface can be diffusive, ballistic, or hydrodynamic. We show that the presence of chiral anomalies, intrinsic to the massless Weyl particles, leads to a hitherto neglected nonlocal regime that can separate the normal and viscous skin effects. We propose to use this regime as a diagnostic of the presence of chiral anomalies in optical conductivity measurements. These results are obtained from a generalized kinetic theory that includes various relaxation mechanisms, allowing us to investigate different transport regimes of Weyl semimetals.

Production of a Chiral Magnetic Anomaly with Emerging Turbulence and Mean-Field Dynamo Action

In relativistic magnetized plasmas, asymmetry in the number densities of left- and right-handed fermions, i.e., a nonzero chiral chemical potential μ_{5}, leads to an electric current along the magnetic field. This causes a chiral dynamo instability for a uniform μ_{5}, but our simulations reveal a dynamo even for fluctuating μ_{5} with zero mean. It produces magnetically dominated turbulence and generates mean magnetic fields via the magnetic α effect. Eventually, a universal scale-invariant k^{-1} spectrum of μ_{5} and a k^{-3} magnetic spectrum are formed independently of the initial condition.

Global Polarization Theory Overview

We give a brief overview about theory development of spin polarization in relativistic heavy ion collisions, which includes how the polarization could be generated by single scattering, what the polarization could be in equilibrium, how to address some recent puzzles in spin polarization in heavy ion collisions and how much progress we have made in spin hydrodynamics and spin kinetic theory. We will also discuss the possible helicity polarization in relativistic heavy ion collisions.

Shear-Induced Spin Polarization in Heavy-Ion Collisions

We study the spin polarization generated by the hydrodynamic gradients. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. We obtain the explicit expression for SIP using the quantum kinetic equation and linear response theory. Based on a realistic hydrodynamic model, we compute the differential spin polarization along both the beam direction z[over ^] and the out-plane direction y[over ^] in noncentral heavy-ion collisions at sqrt[s_{NN}]=200  GeV, including both SIP and thermal vorticity effects. We find that SIP contribution always shows the same azimuthal angle dependence as experimental data and competes with thermal vorticity effects. In the scenario that Λ inherits and memorizes the spin polarization of a strange quark, SIP wins the competition, and the resulting azimuthal angle dependent spin polarization P_{y} and P_{z} agree qualitatively with the experimental data.

Magneto-transport phenomena of type-I multi-Weyl semimetals in co-planar setups

Having the chiral anomaly (CA) induced magneto-transport phenomena extensively studied in single Weyl semimetal as characterized by topological charge n = 1, we here address the transport properties in the context of multi-Weyl semimetals (m-WSMs) where n > 1. Using semiclassical Boltzmann transport formalism with the relaxation time approximation, we investigate several intriguing transport properties such as longitudinal magneto-conductivity (LMC), planar Hall conductivity (PHC), thermo-electric coefficients (TECs) and planar Nernst coefficient (PNC) for m-WSMs in the co-planar setups with external magnetic field, electric field and temperature gradient. Starting from the low-energy model, we show analytically that at zero temperature both LMC and PHC vary cubically with topological charge as n ³ while the finite temperature (T ≠ 0) correction is proportional to (n + n ²)T ². Interestingly, we find that both the longitudinal and transverse TECs vary quadratically with topological charge as n ² and the PNC is found to vary non-monotonically as a function of n. Our study hence clearly suggests that the inherent properties of m-WSMs indeed show up distinctly through the CA and the chiral magnetic effect induced transport coefficients in two different setups. Moreover, in order to obtain an experimentally realizable picture, we simultaneously verify our analytical findings through the numerical calculations using the lattice model of m-WSMs.

Spin Polarizations in a Covariant Angular-Momentum-Conserved Chiral Transport Model

Using a covariant and angular-momentum-conserved chiral transport model, which takes into account the spin-orbit interactions of chiral fermions in their scatterings via the side jumps, we study the quark spin polarization in quark matter. For a system of rotating and unpolarized massless quarks in an expanding box, we find that side jumps can dynamically polarize the quark spin and result in a final quark spin polarization consistent with that of thermally equilibrated massless quarks in a self-consistent vorticity field. For the quark matter produced in noncentral relativistic heavy ion collisions, we find that in the medium rest frame both the quark local spin polarizations in the direction perpendicular to the reaction plane and along the longitudinal beam direction show an azimuthal angle dependence in the transverse plane similar to those observed in experiments for the Lambda hyperon.

Non-perturbative terahertz high-harmonic generation in the three-dimensional Dirac semimetal Cd3As2

Harmonic generation is a general characteristic of driven nonlinear systems, and serves as an efficient tool for investigating the fundamental principles that govern the ultrafast nonlinear dynamics. Here, we report on terahertz-field driven high-harmonic generation in the three-dimensional Dirac semimetal Cd3As2 at room temperature. Excited by linearly-polarized multi-cycle terahertz pulses, the third-, fifth-, and seventh-order harmonic generation is very efficient and detected via time-resolved spectroscopic techniques. The observed harmonic radiation is further studied as a function of pump-pulse fluence. Their fluence dependence is found to deviate evidently from the expected power-law dependence in the perturbative regime. The observed highly non-perturbative behavior is reproduced based on our analysis of the intraband kinetics of the terahertz-field driven nonequilibrium state using the Boltzmann transport theory. Our results indicate that the driven nonlinear kinetics of the Dirac electrons plays the central role for the observed highly nonlinear response.

Topological Semimetal Nanostructures: From Properties to Topotronics

Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.

Acoustogalvanic Effect in Dirac and Weyl Semimetals

The acoustogalvanic effect is proposed as a nonlinear mechanism to generate a direct electric current by passing acoustic waves in Dirac and Weyl semimetals. Unlike the standard acoustoelectric effect, which relies on the sound-induced deformation potential and the corresponding electric field, the acoustogalvanic one originates from the pseudoelectromagnetic fields, which are not subject to screening. The longitudinal acoustogalvanic current scales at least quadratically with the relaxation time, which is in contrast to the photogalvanic current where the scaling is linear. Because of the interplay of pseudoelectric and pseudomagnetic fields, the current could show a nontrivial dependence on the direction of sound wave propagation. Being within the experimental reach, the effect can be utilized to probe dynamical deformations and corresponding pseudoelectromagnetic fields, which are yet to be experimentally observed in Weyl and Dirac semimetals.

Relativistic mechanism of chiral magnetic current in Weyl semimetals with tilted dispersion

The chiral magnetic effect is a one of the exotic bulk transport properties of the Weyl semimetals. Because of the Nielsen-Ninomiya 'no-go theorem', the total chiral magnetic current is absent in the equilibrium state. One of the mechanisms for generating this current is the chiral anomaly. This phenomenon is the anomalous nonconservation of chiral charge for massless relativistic particles. It can be realized by parallel magnetic and electric fields (∼[Formula: see text]), and it leads to such new transport phenomenon as the negative longitudinal magnetoresistance. Using a simple theory (we consider both a linearized and lattice model), we have shown, that in Weyl metals with tilted dispersion another mechanism of the chiral magnetic current is possible. It is not associated with the chiral anomaly. The new transport mechanism is based on the relativistic effect of electric field on Landau levels. This effect is that an electric field changes the distance between the Landau levels, and also changes the effective velocity along magnetic field. At the presence of a tilt in the spectrum, this velocity renormalization is different for different Weyl points. This leads to a non-zero resulting drift velocity. As a consequence, an electrical current arises along the magnetic field. The induced by this mechanism the electric current is proportional to the pseudoscalar product of the fields ([Formula: see text]) and directed along the magnetic field, that differs it from the Hall current (∼[Formula: see text]). At the same time, the conductivity corresponding to this transport mechanism does not depend on the scattering time like the Hall conductivity. Thus, we have proposed a new anomalous transport mechanism in the Weyl semimetal, which is not associated with the chiral anomaly.

Tilting dependence and anisotropy of anomaly-related magnetoconductance in type-II Weyl semimetals

We theoretically study chiral magnetic effect in type-II Weyl semimetals based on a concise formalism for the magnetoconductance in the semiclassical limit. Using the formula, we find that the anomaly-related current is generally dominated by the contribution from the Weyl nodes when the Fermi level is sufficiently close to the nodes. This is related to the fact that the current is proportional to the square of the Berry curvature, which enhances the contribution from the electrons around the Weyl nodes. The increase and the anisotropy of magnetoconductance induced by the tilting is also explained in a comprehensive way.

Dynamical Topological Transitions in the Massive Schwinger Model with a θ Term

Aiming at a better understanding of anomalous and topological effects in gauge theories out of equilibrium, we study the real-time dynamics of a prototype model for CP violation, the massive Schwinger model with a θ term. We identify dynamical quantum phase transitions between different topological sectors that appear after sufficiently strong quenches of the θ parameter. Moreover, we establish a general dynamical topological order parameter, which can be accessed through fermion two-point correlators and, importantly, which can be applied for interacting theories. Enabled by this result, we show that the topological transitions persist beyond the weak-coupling regime. Finally, these effects can be observed with tabletop experiments based on existing cold-atom, superconducting-qubit, and trapped-ion technology. Our Letter thus presents a significant step towards quantum simulating topological and anomalous real-time phenomena relevant to nuclear and high-energy physics.

Strain-induced nonlinear spin Hall effect in topological Dirac semimetal

We show that an electric field applied to a strained topological Dirac semimetal, such as Na₃Bi and Cd₃As₂, induces a spin Hall current that is quadratic in the electric field. By regarding the strain as an effective "axial magnetic field" for the Dirac electrons, we investigate the electron and spin transport semiclassically in terms of the chiral kinetic theory. The nonlinear spin Hall effect arises as the cross effect between the regular Hall effect driven by the axial magnetic field and the anomalous Hall effect coming from the momentum-space topology. It provides an efficient way to generate a fully spin-polarized and rectified spin current out of an alternating electric field, which is sufficiently large and can be directly tuned by the gate voltage and the strain.

Berry phase theory of planar Hall effect in topological insulators

The appearance of negative longitudinal magnetoresistance (LMR) in topological semimetals such as Weyl and Dirac semimetals is understood as an effect of chiral anomaly, whereas such an anomaly is not well-defined in topological insulators. Nevertheless, it has been shown recently in both theory and experiments that nontrivial Berry phase effects can give rise to negative LMR in topological insulators even in the absence of chiral anomaly. In this paper, we present a quasi-classical theory of another intriguing phenomenon in topological insulators - also ascribed to chiral anomaly in Weyl and Dirac semimetals- the so-called planar Hall effect (PHE). PHE implies the appearance of a transverse voltage in the plane of applied non-parallel electric and magnetic fields, in a configuration in which the conventional Hall effect vanishes. Starting from Boltzmann transport equations we derive the expressions for PHE and LMR in topological insulators in the bulk conduction limit, and show the important role played by orbital magnetic moment. Our theoretical results for magnetoconductance with non-parallel electric and magnetic fields predict detailed experimental signatures in topological insulators - specifically of planar Hall effect - that can be observed in experiments.

Collective excitations in Weyl semimetals in the hydrodynamic regime

The spectrum of collective excitations in Weyl materials is studied by using consistent hydrodynamics. The corresponding framework includes the vortical and chiral anomaly effects, as well as the dependence on the separations between the Weyl nodes in energy b ₀ and momentum [Formula: see text]. The latter are introduced via the Chern-Simons contributions to the electric current and charge densities in Maxwell's equations. It is found that, even in the absence of a background magnetic field, certain collective excitations (e.g. the helicon-like modes and the anomalous Hall waves) are strongly affected by the chiral shift [Formula: see text]. In a background magnetic field, the existence of the distinctive longitudinal and transverse anomalous Hall waves with a linear dispersion relation is predicted. They originate from the oscillations of the electric charge density and electromagnetic fields, in which different components of the fields are connected via the anomalous Hall effect in Weyl semimetals.

Violation of Ohm's law in a Weyl metal

Ohm's law is a fundamental paradigm in the electrical transport of metals. Any transport signatures violating Ohm's law would give an indisputable fingerprint for a novel metallic state. Here, we uncover the breakdown of Ohm's law owing to a topological structure of the chiral anomaly in the Weyl metal phase. We observe nonlinear I-V characteristics in Bi_0.96Sb_0.04 single crystals in the diffusive limit, which occurs only for a magnetic-field-aligned electric field (E∥B). The Boltzmann transport theory with the charge pumping effect reveals the topological-in-origin nonlinear conductivity, and it leads to a universal scaling function of the longitudinal magnetoconductivity, which completely describes our experimental results. As a hallmark of Weyl metals, the nonlinear conductivity provides a venue for nonlinear electronics, optical applications, and the development of a topological Fermi-liquid theory beyond the Landau Fermi-liquid theory.

Consistent Chiral Kinetic Theory in Weyl Materials: Chiral Magnetic Plasmons

We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern-Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields, taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also by oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. This finding suggests an efficient means of extracting the chiral shift parameter from the measurement of the plasma frequencies in Weyl materials.

Chiral Magnetic Effect and Anomalous Transport from Real-Time Lattice Simulations

We present a first-principles study of anomaly induced transport phenomena by performing real-time lattice simulations with dynamical fermions coupled simultaneously to non-Abelian SU(N_{c}) and Abelian U(1) gauge fields. Investigating the behavior of vector and axial currents during a sphaleron transition in the presence of an external magnetic field, we demonstrate how the interplay of the chiral magnetic and chiral separation effect leads to the formation of a propagating wave. We further analyze the dependence of the magnitude of the induced vector current and the propagation of the wave on the amount of explicit chiral symmetry breaking due to finite quark masses.

Magnetic Shift of the Chemical Freeze-out and Electric Charge Fluctuations

We discuss the effect of a strong magnetic field on the chemical freeze-out points in ultrarelativistic heavy-ion collisions. As a result of inverse magnetic catalysis or magnetic inhibition, the crossover onset to hot and dense matter out of quarks and gluons should be shifted to a lower temperature. To quantify this shift we employ the hadron resonance gas model and an empirical condition for the chemical freeze-out. We point out that the charged particle abundances are significantly affected by the magnetic field so that the electric charge fluctuation is largely enhanced, especially at high baryon density. The charge conservation partially cancels the enhancement, but our calculation shows that the electric charge fluctuation could serve as a magnetometer. We find that the fluctuation exhibits a crossover behavior rapidly increased for eB≳(0.4  GeV)^{2}, while the charge chemical potential has smoother behavior with an increasing magnetic field.

Electromagnetic fields and anomalous transports in heavy-ion collisions-a pedagogical review

The hot and dense matter generated in heavy-ion collisions may contain domains which are not invariant under P and CP transformations. Moreover, heavy-ion collisions can generate extremely strong magnetic fields as well as electric fields. The interplay between the electromagnetic field and triangle anomaly leads to a number of macroscopic quantum phenomena in these P- and CP-odd domains known as anomalous transports. The purpose of this article is to give a pedagogical review of various properties of the electromagnetic fields, the anomalous transport phenomena, and their experimental signatures in heavy-ion collisions.

Simulating Chiral Magnetic and Separation Effects with Spin-Orbit Coupled Atomic Gases

The chiral magnetic and chiral separation effects-quantum-anomaly-induced electric current and chiral current along an external magnetic field in parity-odd quark-gluon plasma-have received intense studies in the community of heavy-ion collision physics. We show that analogous effects occur in rotating trapped Fermi gases with Weyl-Zeeman spin-orbit coupling where the rotation plays the role of an external magnetic field. These effects can induce a mass quadrupole in the atomic cloud along the rotation axis which may be tested in future experiments. Our results suggest that the spin-orbit coupled atomic gases are potential simulators of the chiral magnetic and separation effects.

Chiral Alfvén Wave in Anomalous Hydrodynamics

We study the hydrodynamic regime of chiral plasmas at high temperature. We find a new type of gapless collective excitation induced by chiral effects in an external magnetic field. This is a transverse wave, and it is present even in incompressible fluids, unlike the chiral magnetic and chiral vortical waves. The velocity is proportional to the coefficient of the gravitational anomaly. We briefly discuss the possible relevance of this "chiral Alfvén wave" in physical systems.

Wigner translations and the observer dependence of the position of massless spinning particles

The Wigner little group for massless particles is isomorphic to the Euclidean group SE(2). Applied to momentum eigenstates, or to infinite plane waves, the Euclidean "Wigner translations" act as the identity. We show that when applied to finite wave packets, the translation generators move the packet trajectory parallel to itself through a distance proportional to the particle's helicity. We relate this effect to the spin Hall effect of light and to the Lorentz-frame dependence of the position of a massless spinning particle.

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

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 the physics of strong spin-orbit coupling, although the concept of electron quasiparticles remains valid near the Fermi surface, where Landau's Fermi-liquid theory fails to describe the 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 the Berry curvature and the 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 [Formula: see text] term. This novel metallic state was realized recently in Bi[Formula: see text]Sb _x around [Formula: see text] under magnetic fields, where the Dirac spectrum appears around the critical point between the normal semiconducting ([Formula: see text]) and topological semiconducting phases ([Formula: see text]) 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 a very strong spin-orbit coupled system. In this review article, we discuss how the topological structure of both the Berry curvature and the chiral anomaly (axion electrodynamics) gives rise to anomalous transport phenomena in [Formula: see text]Sb _x around [Formula: see text] under magnetic fields, thus modifying the Drude model of Landau's Fermi liquids.

Lorentz invariance in chiral kinetic theory

We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-1/2 particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum. The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lorentz-invariant kinetic theory due to side jumps. We show that 2/3 of the chiral-vortical effect for a uniformly rotating particle distribution can be attributed to the magnetic moment coupling required by the Lorentz invariance. We also show how the classical action can be obtained by taking the classical limit of the path integral for a Weyl particle.

Chiral and gravitational anomalies on Fermi surfaces

A Fermi surface threaded by a Berry phase can be described by the Wess-Zumino-Witten term. After gauging, it produces a five-dimensional Chern-Simons term in the action. We show how this Chern-Simons term captures the essence of the Abelian, non-Abelian, and mixed gravitational anomalies in describing both in- and off-equilibrium phenomena. In particular, we derive a novel contribution to the chiral vortical effect that arises when a temperature gradient is present. We also discuss the issue of universality of the anomalous currents.

Chiral plasma instabilities

We study the collective modes in relativistic electromagnetic or quark-gluon plasmas with an asymmetry between left- and right-handed chiral fermions, based on the recently formulated kinetic theory with Berry curvature corrections. We find that there exists an unstable mode, signaling the presence of a plasma instability. We argue the fate of this "chiral plasma instability" including the effect of collisions, and briefly discuss its relevance in heavy ion collisions and compact stars.

Berry curvature and four-dimensional monopoles in the relativistic chiral kinetic equation

We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a four-dimensional Euclidean Berry monopole which gives an axial anomaly. By integrating out the zeroth component of the 4-momentum p, we reproduce the previous three-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields (FσρF[over ˜]σρ∼EσBσ). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.

Axial current generation from electric field: chiral electric separation effect

We study a relativistic plasma containing charged chiral fermions in an external electric field. We show that with the presence of both vector and axial charge densities, the electric field can induce an axial current along its direction and thus cause chirality separation. We call it the chiral electric separation effect (CESE). On a very general basis, we argue that the strength of CESE is proportional to μ(V)μ(A) with μ(V) and μ(A) the chemical potentials for vector charge and axial charge. We then explicitly calculate this CESE conductivity coefficient in thermal QED at leading-log order. The CESE can manifest a new gapless wave mode propagating along the electric field. Potential observable effects of CESE in heavy-ion collisions are also discussed.