Chiral Magnetic Conductivity Research Articles

Effect of electric and chiral magnetic conductivities on azimuthally fluctuating electromagnetic fields and observables in isobar collisions

Effect of electric and chiral magnetic conductivities on azimuthally fluctuating electromagnetic fields and observables in isobar collisions

Chiral Light Amplifier with Pumped Weyl Semimetals.

Parallel electric and magnetic fields applied to Weyl semimetals pump axial charge via the axial anomaly until balanced by intervalley relaxation. The resulting nonequilibrium steady state exhibits the chiral magnetic effect as well as the anomalous Hall effect, which coupled with Maxwell's equations leads to unstable electromagnetic waves at low frequency and long wavelength. Here, we show that such chiral magnetic instability manifests itself as anomalous reflectance of the surface of pumped Weyl semimetal. Depending on electric, chiral magnetic, and anomalous Hall conductivities, the reflectance is found to exceed unity in a finite range of frequency for a circularly polarized light incident along the direction of Weyl node separation.

Dynamical chiral magnetic current and instability in Weyl semimetals

Weyl semimetals realize massless relativistic fermions with two Weyl nodes separated in energy and momentum space, whose low-energy physics is described by Dirac fermions with an axial gauge constant. Here, we study their electromagnetic linear responses based on the effective field theory and on the chiral kinetic theory. Although the static chiral magnetic effect is canceled by the Chern-Simons current under the Pauli-Villars regularization, a dynamical magnetic field is found capable of driving an electric current along its direction, with the total transported charge being independent of temperature and chemical potential for a uniform field. We also incorporate dissipation in the relaxation-time approximation and study collective excitations coupled with Maxwell electromagnetic fields when Weyl node populations deviate from equilibrium. Their dispersion relations at low frequency and long wavelength are determined only by electric, chiral magnetic, and anomalous Hall conductivities, which predict unstable modes leading to anisotropic generation of electromagnetic waves oriented to the direction of Weyl node separation.

Chiral magnetic effect out of equilibrium

We consider relativistic fermionic systems in lattice regularization out of equilibrium. The chiral magnetic conductivity ${\ensuremath{\sigma}}_{\mathrm{CME}}$ is calculated in a spatially infinite system for the case when the chiral chemical potential depends on time, while the system initially was in thermal equilibrium at a small but nonzero temperature. We find that the frequency-dependent ${\ensuremath{\sigma}}_{\mathrm{CME}}(\ensuremath{\omega})$ for any nonzero $\ensuremath{\omega}$ both in the limits $\ensuremath{\omega}\ensuremath{\ll}T$ and $\ensuremath{\omega}\ensuremath{\gg}T$ is equal to its conventional value 1 when the lattice model approaches the continuum limit. Notice that ${\ensuremath{\sigma}}_{\mathrm{CME}}=0$ for the case when the chiral chemical potential does not depend on time at all. We therefore confirm that the limit of vanishing $\ensuremath{\omega}$ is not regular for the spatially infinite systems of massless fermions.

Bremsstrahlung in chiral medium: Anomalous magnetic contribution to the Bethe-Heitler formula

We investigate photon bremsstrahlung in chiral media. The chiral medium response to the magnetic field is described by the chiral magnetic current $\mathbit{j}={b}_{0}\mathbit{B}$, where ${b}_{0}$ is the chiral magnetic conductivity. This current modifies the photon dispersion relation producing a resonance in the scattering amplitude. We show that the resonant contribution is proportional to the magnetic moment $\ensuremath{\mu}$ of the target nucleus. We analytically compute the corresponding cross section. We argue that the anomalous contribution is enhanced by a factor ${b}_{0}^{2}/{\mathrm{\ensuremath{\Gamma}}}^{2}$, where $\mathrm{\ensuremath{\Gamma}}$ is a width of the resonance related to the chiral magnetic instability of the electromagnetic field. The most conspicuous feature of the anomalous contribution to the photon spectrum is the emergence of the kneelike structure at photon energies proportional to ${b}_{0}$. We argue that the phenomenological significance of the anomalous terms depends on the magnitude of the ratio of ${b}_{0}$ to the projectile fermion mass.

Electromagnetic anomaly in the presence of electric and chiral magnetic conductivities in relativistic heavy-ion collisions

We study the spacetime evolution of electric $(\textbf{E})$ and magnetic $(\textbf{B})$ fields along with the electromagnetic anomaly $(\textbf{E}\cdot\textbf{B})$ in the presence of electric ($\sigma$) and chiral magnetic ($\sigma_{\chi}$) conductivities in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$~GeV. By comparing to the Lienard-Wiechert solutions with zero conductivities, we observe a symmetry breaking of the electromagnetic field in a conducting medium with respect to the reaction plane. The decay of the field is also significantly decelerated after the conductivities are introduced. Similar effects are also found for the dipole structure of $\textbf{E}\cdot\textbf{B}$ as well as the quadrupole structure of $(\textbf{E}\cdot\textbf{B})\textbf{B}$, which may finally affect the charge separation of the elliptic flow coefficient of hadrons observed in high-energy nuclear collisions.

Equilibrium chiral magnetic effect: Spatial inhomogeneity, finite temperature, interactions

We discuss equilibrium relativistic fermionic systems in lattice regularization, and extend the consideration of chiral magnetic effect to systems with spatial inhomogeneity and finite temperature. Besides, we take into account interactions due to exchange by gauge bosons. We find that the equilibrium chiral magnetic conductivity remains equal to zero.

Chiral magnetic response to arbitrary axial imbalance

The response of chiral fermions to time and space dependent axial imbalance & constant magnetic field is analyzed. The axialvector-vector-vector (AVV) three-point function is studied using a real-time approach at finite temperature in the weak external field approximation. The chiral magnetic conductivity is given analytically for noninteracting fermions. It is pointed out that local charge conservation plays an important role when the axial imbalance is inhomogeneous. Proper regularization is needed which makes the constant axial imbalance limit delicate: for static but spatially oscillating chiral charge the current of the chiral magnetic effect (CME) vanishes. In the homogeneous (but possible time-dependent) limit of the axial imbalance the CME current is determined solely by the chiral anomaly. As a phenomenological consequence, the observability of the charge asymmetry caused by the CME turns out to be a matter of interplay between various scales of the system. Possible plasma instabilities resulting from the gradient corrections to the CME current are also pointed out.

Magnetic fields in heavy ion collisions: flow and charge transport

At the earliest times after a heavy-ion collision, the magnetic field created by the spectator nucleons will generate an extremely strong, albeit rapidly decreasing in time, magnetic field. The impact of this magnetic field may have detectable consequences, and is believed to drive anomalous transport effects like the Chiral Magnetic Effect (CME). We detail an exploratory study on the effects of a dynamical magnetic field on the hydrodynamic medium created in the collisions of two ultrarelativistic heavy-ions, using the framework of numerical ideal MagnetoHydroDynamics (MHD) with the ECHO-QGP code. In this study, we consider a magnetic field captured in a conducting medium, where the conductivity can receive contributions from the electromagnetic conductivity sigma and the chiral magnetic conductivity sigma _{chi }. We first study the elliptic flow of pions, which we show is relatively unchanged by the introduction of a magnetic field. However, by increasing the magnitude of the magnetic field, we find evidence for an enhancement of the elliptic flow in peripheral collisions. This effect is stronger at RHIC than the LHC, and it is evident already at intermediate collision centralities. Next, we explore the impact of the chiral magnetic conductivity on electric charges produced at the edges of the fireball. This initial sigma _chi can be understood as a long-wavelength effective description of chiral fermion production. We then demonstrate that this chiral charge, when transported by the MHD medium, produces a charge dipole perpendicular to the reaction plane which extends a few units in rapidity. Assuming charge conservation at the freeze-out surface, we show that the produced charge imbalance can have measurable effects on some experimental observables, like v_1 or langle sin phi rangle . This demonstrates the ability of a MHD fluid to transport the signature of the initial chiral magnetic fields to late times. We also comment on the limitations of the ideal MHD approximation and detail how further development of a dissipative-resistive model can provide a more realistic description of the QGP.

Dynamic chiral magnetic effect and anisotropic natural optical activity of tilted Weyl semimetals

We study the dynamic chiral magnetic conductivity (DCMC) and natural optical activity in an inversion-broken tilted Weyl semimetal (WSM). Starting from the Kubo formula, we derive the analytical expressions for the DCMC for two different directions of the incident electromagnetic wave. We show that the angle of rotation of the plane of polarization of the transmitted wave exhibits remarkable anisotropy and is larger along the tilt direction. This striking anisotropy of DCMC results in anisotropic optical activity and rotary power, which can be experimentally observed as a topological magneto-electric effect of inversion-broken tilted WSMs. Finally, using the low energy Hamiltonian, we show that the DCMC follows the universal frac{{bf{1}}}{{{boldsymbol{omega }}}^{{bf{2}}}} decay in the high frequency regime. In the low frequency regime, however, the DCMC shows sharp peaks at the tilt dependent effective chemical potentials of the left-handed and right-handed Weyl points. This can serve as a signature to distinguish between the type-I and type-II Weyl semimetals.

Anomalous magnetohydrodynamics with longitudinal boost invariance and chiral magnetic effect

We study relativistic magnetohydrodynamics with longitudinal boost invariance in the presence of chiral magnetic effects and finite electric conductivity. With initial magnetic fields parallel or anti-parallel to electric fields, we derive the analytic solutions of electromagnetic fields and the chiral number and energy density in an expansion of several parameters determined by initial conditions. The numerical solutions show that such analytic solutions work well in weak fields or large chiral fluctuations. We also discuss the properties of electromagnetic fields in the laboratory frame.

Chiral transport in strong fields from holography

Anomaly-induced transport phenomena in presence of strong external electromagnetic fields are explored within a 4D field theory defined holographically as U(1)V × U(1)A Maxwell-Chern-Simons theory in Schwarzschild-AdS5. Two complementary studies are reported. In the first one, we present results on the Ohmic conductivity, diffusion constant, chiral magnetic conductivity, and additional anomaly-induced transport coefficients as functions of external e/m fields. Next, gradient resummation in a constant background magnetic field is performed. All-order resummed constitutive relations are parameterised by four momenta-dependent transport coefficient functions (TCFs). A highlight of this part is a thorough study of non-dissipative chiral magnetic waves (CMW) in strong magnetic fields.

Rotating solutions of nonideal transverse Chern-Simons magnetohydrodynamics

In order to gain deeper insight into the physics of the novel rotating solution of nonideal transverse magnetohydrodynamics (MHD), presented in one of our recent works, we replace the previously considered Maxwell theory with the ${\cal{CP}}$ violating Maxwell-Chern-Simons (MCS) theory. In this way, dissipationless chiral magnetic (CM) and anomalous Hall (AH) currents appear in the MCS equation of motion, that, together with equations of relativistic hydrodynamics, builds the set of constitutive equations of the nonideal transverse Chern-Simons magnetohydrodynamics (CSMHD). We are, in particular, interested in the effect of these currents on the evolution of electromagnetic fields in a uniformly and longitudinally expanding quark-gluon plasma with chirality imbalance. Combining the constitutive equations of CSMHD under these assumptions, we arrive, as expected, at two distinct rotating and nonrotating solutions for electromagnetic fields. The rotation occurs with increasing rapidity and a constant angular velocity $\omega_{0}$. Remarkably, the relative angle between the electric and magnetic fields, $\delta$, turns out to be given by the coefficient of AH current $\kappa_{E}$ and the electric conductivity of the medium $\sigma$, as $\delta=\tan^{-1}(\kappa_{E}/\sigma)$. Whereas the nonrotating solution implies the AH coefficient to be vanishing, and thus nonrotating electric and magnetic fields to be either parallel or antiparallel, the relative orientation of rotating electric and magnetic fields and the evolution of the CM conductivity $\kappa_{B}$ are strongly affected by nonvanishing $\kappa_{E}$. We explore the effect of positive and negative $\omega_{0}$ on the evolution of the CM current, and show, in particular, that a rotation of electromagnetic fields with negative $\omega_{0}$ implies a sign flip of the CM current in a chiral fluid with nonvanishing AH current.

On magnetostatics of chiral media

We consider magnetostatics of chiral media with a non-vanishing chiral chemical potential μ5≠0. In such media, the chiral anomaly has macroscopic manifestations which go beyond the standard classical electrodynamics. A new term in the effective action takes form of a topological three-dimensional photon mass. The topological mass turns to be imaginary and signals instability. Namely, magnetic field with non-trivial helicity is generated spontaneously. A stable state corresponds to a solution of the Beltrami equations. From the action relevant to instability, we show also that the interaction between two current loops reduces to the linking number of the loops. In addition, we observe the vanishing of the chiral magnetic conductivity in the strict static and uniform limit.

Dynamical correlation functions and the related physical effects in three-dimensional Weyl/Dirac semimetals

We present a unified derivation of the dynamical correlation functions including density-density, density-current and current-current, of three-dimensional Weyl/Dirac semimetals by use of the Passarino-Veltman reduction scheme at zero temperature. The generalized Kramers-Kronig relations with arbitrary order of subtraction are established to verify these correlation functions. Our results lead to the exact chiral magnetic conductivity and directly recover the previous ones in several limits. We also investigate the magnetic susceptibilities, the orbital magnetization and briefly discuss the impact of electron interactions on these physical quantities within the random phase approximation. Our work could provide a starting point for the investigation of the nonlocal transport and optical properties due to the higher-order spatial dispersion in three-dimensional Weyl/Dirac semimetals.

Anomalous transport and holographic momentum relaxation

The chiral magnetic and vortical effects denote the generation of dissipationless currents due to magnetic fields or rotation. They can be studied in holographic models with Chern-Simons couplings dual to anomalies in field theory. We study a holographic model with translation symmetry breaking based on linear massless scalar field backgrounds. We compute the electric DC conductivity and find that it can vanish for certain values of the translation symmetry breaking couplings. Then we compute the chiral magnetic and chiral vortical conductivities. They are completely independent of the holographic disorder couplings and take the usual values in terms of chemical potential and temperature. To arrive at this result we suggest a new definition of energy-momentum tensor in presence of the gravitational Chern-Simons coupling.

Quantum oscillations in the chiral magnetic conductivity

In strong magnetic field the longitudinal magnetoconductivity in 3D chiral materials is shown to exhibit a new type of quantum oscillations arising from the chiral magnetic effect (CME). These quantum CME oscillations are predicted to dominate over the Shubnikov-de Haas (SdH) ones in chiral materials with an approximately conserved chirality of quasiparticles at strong magnetic fields. The phase of quantum CME oscillations differs from the phase of the conventional SdH oscillations by $\pi/2$.

Anatomy of the chiral magnetic effect in and out of equilibrium

We identify a new contribution to the chiral magnetic conductivity at finite frequencies -- the magnetization current. This allows to quantitatively reproduce the known field-theoretic time-dependent (AC) chiral magnetic response in terms of kinetic theory. We evaluate the corresponding AC chiral magnetic conductivity in two flavor QCD plasma at weak coupling. The magnetization current results from the spin response of chiral quasiparticles to magnetic field, and is thus proportional to the quasiparticle's $g$-factor. In condensed matter systems, where the chiral quasi-particles are emergent and the $g$-factor can significantly differ from 2, this opens the possibility to tune the AC chiral magnetic response.

Dynamic Chiral Magnetic Effect and Faraday Rotation in Macroscopically Disordered Helical Metals.

We develop an effective medium theory for electromagnetic wave propagation through gapless nonuniform systems with a dynamic chiral magnetic effect. The theory allows us to calculate macroscopic-disorder-induced corrections to the values of optical, as well as chiral magnetic conductivities. In particular, we show that spatial fluctuations of the optical conductivity induce corrections to the effective value of the chiral magnetic conductivity. The absolute value of the effect varies strongly depending on the system parameters, but yields the leading frequency dependence of the polarization rotation and circular dichroism signals. Experimentally, these corrections can be observed as features in the Faraday rotation angle near frequencies that correspond to the bulk plasmon resonances of a material. Such features are not expected to be present in single-crystal samples.

Electromagnetic fields with electric and chiral magnetic conductivities in heavy ion collisions

We derive analytic formula for electric and magnetic fields produced by a moving charged particle in a conducting medium with the electric conductivity $\sigma$ and the chiral magnetic conductivity $\sigma_{\chi}$. We use the Green function method and assume that $\sigma_{\chi}$ is much smaller than $\sigma$. The compact algebraic expressions for electric and magnetic fields without any integrals are obtained. They recover the Lienard-Wiechert formula at vanishing conductivities. Exact numerical solutions are also found for any values of $\sigma$ and $\sigma_{\chi}$ and are compared to analytic results. Both numerical and analytic results agree very well for the scale of high energy heavy ion collisions. The space-time profiles of electromagnetic fields in non-central Au+Au collisions have been calculated based on these analytic formula as well as exact numerical solutions.