Chiral Vortical Effect Research Articles

Anomalous chiral transports and spin polarization in heavy-ion collisions

Relativistic heavy-ion collisions create hot quark-gluon plasma as well as very strong electromagnetic (EM) and fluid vortical fields. The strong EM field and vorticity can induce intriguing macroscopic quantum phenomena such as chiral magnetic, chiral separation, chiral electric separation, and chiral vortical effects as well as the spin polarization of hadrons. These phenomena provide us with experimentally feasible means to study the nontrivial topological sector of quantum chromodynamics, the possible parity violation of strong interaction at high temperature, and the subatomic spintronics of quark-gluon plasma. These studies, both in theory and in experiments, are strongly connected with other subfields of physics such as condensed matter physics, astrophysics, and cold atomic physics, and thus form an emerging interdisciplinary research area. We give an introduction to the aforementioned phenomena induced by the EM field and vorticity and an overview of the current status of their experimental research in heavy-ion collisions. We also briefly discuss spin hydrodynamics as well as chiral and spin kinetic theories.

Magneto-vortical effect in strongly coupled plasma

Based on a holographic model incorporating both the chiral anomaly and the gravitational anomaly, we study the effect of magneto-vortical coupling on the transport properties of a strongly coupled plasma. The focus of present work is on the generation of a vector charge density and an axial current, as response to vorticity in a magnetized plasma. The transport coefficients parameterizing the vector charge density and axial current are calculated both analytically (in the weak magnetic field limit) and also numerically (for general values of the magnetic field). We find the generation of vector charge receives both non-anomalous and anomalous contributions, with the non-anomalous contribution dominating in the limit of a strong magnetic field and the anomalous contribution sensitive to both chiral anomaly and gravitational anomaly. On the contrary, we find the axial current is induced entirely due to the gravitational anomaly, thus we interpret the axial current generation as chiral vortical effect. The corresponding chiral vortical conductivity is found to be suppressed by the magnetic field. By the Onsager relation, these transport coefficients are responsible for the generation of a thermal current due to a transverse electric field or a transverse axial magnetic field, which we call the thermal Hall effect and the thermal axial magnetic effect, respectively.

Chiral Magnetic Effects in Nuclear Collisions

The interplay of quantum anomalies with strong magnetic fields and vorticity in chiral systems could lead to novel transport phenomena, such as the chiral magnetic effect (CME), the chiral magnetic wave (CMW), and the chiral vortical effect (CVE). In high-energy nuclear collisions, these chiral effects may survive the expansion of a quark–gluon plasma fireball and be detected in experiments. The experimental searches for the CME, the CMW, and the CVE have aroused extensive interest over the past couple of decades. The main goal of this article is to review the latest experimental progress in the search for these novel chiral transport phenomena at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory and the Large Hadron Collider at CERN. Future programs to help reduce uncertainties and facilitate the interpretation of the data are also discussed.

Chiral vortical and Chiral torsional effects

Corrections to the chiral vortical effect due to the finite volume and the presence of mass are discussed. The possibility to describe the chiral vortical effect(CVE) by an effective gauge field is considered. The new chiral effect arising in the presence of torsion is described.

Quantum Field Effects of Acceleration and Rotation: the Chiral Vortical Effect and the Unruh Effect

The effects of vorticity and acceleration can be studied in the framework of a general fundamental approach based on the Zubarev density operator. The calculation of axial current is related to Chiral Vortical Effect (CVE) and hyperon polarization, while the calculation of acceleration corrections to energy density leads to the Unruh effect. The nonperturbative formula for CVE of massive fermions and the possibility of stabilization and suppression of the axial current in the plasma of elementary particles due to the appearance of an effective mass, depending on temperature, is discussed.

Contribution of the chiral vortical effect to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the early Universe

In this paper, we study the contribution of the chiral vortical effect, in addition to that of the chiral magnetic effect, to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the symmetric phase of the early Universe in the temperature range 100GeV < T < 10TeV. We choose a fully helical Chern-Simons wave configuration for the velocity and the hypermagnetic vector potential fields. The latter makes the plasma force-free in the absence of viscosity. We show that the most pronounced effect of the chiral vorticity is the production and initial growth of the hypermagnetic field. In particular, we show that in the presence of a non-zero matter asymmetry, the hypermagnetic field can grow from zero initial value only in the presence of a non-zero vorticity field. Moreover, we show that larger initial growths not only result in larger maximum values of the hypermagnetic field, but also cause the saturation of the hypermagnetic field and the conversion of the lepton-baryon asymmetry to occur more quickly, i.e., at a higher temperature. We show that the damping of the vorticity due to the presence of viscosity, which typically occurs extremely rapidly, does not significantly affect the evolution.

Anomalous currents and constitutive relations of a chiral hadronic superfluid

The anomalous currents of two-flavor chiral nuclear matter in the presence of chiral imbalance are computed, using recently developed methods exploiting generalized transgression, which facilitates the evaluation of both the equilibrium partition function and the covariant currents. The constitutive relations for both the broken and unbroken phase of the theory are studied and the out-of-equilibrium nondissipative transport coefficients determined. In the superfluid phase, the vector covariant currents exhibit nondissipative chiral electric, magnetic, and vortical effects, the latter governed by chiral imbalance.

Chiral vortical effect in Wigner function approach

It is more subtle to obtain the chiral vortical effect (CVE) than chiral magnetic effect (CME) in quantum transport approach. To investigate the subtlty of the CVE we present two different derivation in the Wigner function approach. The first one is based on the method in our previous work \cite{Gao:2012ix} in which the CVE was derived under static-equilibrium conditions without details. We provide a detailed derivation using a more transparent and powerful method, which can be easily generalized to higher order calculation. In this derivation of the CVE current, there is an explicit Lorentz covariance. The second derivation is based on a more general chiral kinetic theory in a semi-classical expansion of the Wigner function without assuming static-equilibrium conditions \cite{Gao:2018wmr}. In this derivation, there is a freedom to choose a reference frame for the CVE current, so the explicit Lorentz covariance seems to be lost. Howerver, under static-equilibrium conditions, we show that the CVE current in this derivation can be decomposed into two parts, identified as the normal and magnetization current. Each part depends on the reference frame, but the sum of two parts does give the total CVE current which is independent of the reference frame. In the comoving frame of the fluid, it can be shown that the normal and magnetization current give one-third and two-thirds of the total CVE current respectively. This gives a natural solution to the 'one-third' puzzle in the CVE current in three-dimensional version of the chiral kinetic theory in the literature.

Magnetovortical and thermoelectric transport in tilted Weyl metals

We investigate how tilting affects the off-diagonal, dissipationless response of a pair of chirally imbalanced Weyl cones to various external perturbations. The pair of chirally imbalanced Weyl cones can be described as a chiral electron fluid, that can flow with a velocity field that contains vorticity. Upon applying an external magnetic field, we obtain the so-called magnetovortical linear-response matrix that relates electric and heat currents to the magnetic field (chiral magnetic effect) and the vorticity (chiral vortical effect). We show how this reponse matrix becomes anisotropic upon tilting the cones and determine its non-analytic long-wavelength behavior, as well as the corresponding AC response. In addition, we discuss how the tilt dependence of the electronic (or density-density) susceptibility introduces anisotropy in the dispersion relation of the sound-like excitations in the fluid of chiral fermions, which are known as chiral magnetic waves. In the case of an externally applied electric field and a temperature gradient, we find a Hall-like response in the electric and heat current density that is perpendicular to both the tilting direction and the perturbations. As the tilting direction forms a time-reversal symmetry breaking vector, a non-zero (heat) orbital magnetization manifests itself. We calculate the magnetization currents microscopically and elucidate how to subtract these contributions to obtain the transport currents.

Chiral kinetic theory in curved spacetime

Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect (CVE). We also show that the CVE is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of observer's frame.

Torsional response and Liouville anomaly in Weyl semimetals with dislocations

Weyl nodes in three-dimensional Weyl semimetals break the Liouville equation, leading to the Liouville anomaly. Here we present a new approach to derive the semiclassical action and equations of motion for Weyl fermions in the presence of electromagnetic fields and torsions from the quantum field theory: combining the Wigner transformation with band projection operation. It has been shown that the Liouville anomaly, including a new pure torsion anomaly term, a mixing term between the electromagnetic fields and torsions as well as the conventional chiral anomaly, entirely differs from the counterpart of axial gauge fields. We find various torsional responses and reproduce the chiral vortical effect and the torsional chiral magnetic effect. A new torsion modified anomalous Hall effect due to the mixing term in the Liouville anomaly is predicted and its implementation is also discussed. Therefore, our work not only provides new insights into the torsional responses for Weyl fermions but also acts as a starting point to investigate their topological responses.

Chiral vortical effect for an arbitrary spin

The spin Hall effect of light attracted enormous attention in the literature due to the ongoing progress in developing of new optically active materials and metamaterials with non-trivial spin-orbit interaction. Recently, it was shown that rotating fermionic systems with relativistic massless spectrum may exhibit a 3-dimensional analogue of the spin Hall current — the chiral vortical effect (CVE). Here we show that CVE is a general feature of massless particles with an arbitrary spin. We derive the semi-classical equations of motion in rotating frame from the first principles and show how by coordinate transformation in the phase space it can be brought to the intuitive form proposed in [1]. Our finding clarifies the superficial discrepancies in different formulations of the chiral kinetic theory for rotating systems. We then generalize the chiral kinetic theory, originally introduced for fermions, to an arbitrary spin and study chirality current in a general rotating chiral medium. We stress that the higher-spin realizations of CVE can be in principle observed in various setups including table-top experiments on quantum optics.

Effects of rotation and acceleration in the axial current: density operator vs Wigner function

The hydrodynamic coefficients in the axial current are calculated on the basis of the equilibrium quantum statistical density operator in the third order of perturbation theory in thermal vorticity tensor both for the case of massive and massless fermions. The coefficients obtained describe third-order corrections to the Chiral Vortical Effect and include the contribution from local acceleration. We show that the methods of the Wigner function and the statistical density operator lead to the same result for an axial current in describing effects associated only with vorticity when the local acceleration is zero, but differ in describing mixed effects for which both acceleration and vorticity are significant simultaneously.

Polarization in HIC: comparison of methods

Based on the Wigner function for an medium with thermal vorticity, an exact non-perturbative formula for axial current was obtained. It is confirmed that the Chiral Vortical Effect results from the Wigner function. It is shown that the angular velocity and acceleration play the role of new chemical potentials, which is expressed in the appearance of combination $$\mu \pm \,(\Omega \pm i\left| a \right|)/2$$. It is shown that acceleration enters in the form of imaginary chemical potential and the consequences of this fact are investigated. An expression for the boundary temperature for a medium of fermions, which simultaneously has acceleration and rotation, is derived. This temperature in the particular case coincides with the temperature of Unruh.

Mass correction to chiral vortical effect and chiral separation effect

We study coefficients of axial chiral vortical effect and chiral separation effect at finite temperature and vector chemical potential in massive theories. We present two independent methods of calculating the coefficients: one from field theory and the other using the mass term in axial anomaly equation. An ambiguity in the integration constant similar to hydrodynamic approach to axial chiral vortical effect exists in the latter, but can be fixed naturally in the presence of mass. We obtain perfect agreement between the methods. The results of axial chiral vortical effect and chiral separation effect indicate that the presence of mass generically suppresses the two coefficients, with less suppression at larger chemical potential. For phenomenologically relevant case of quark gluon plasma with three quark flavor, we find the correction is negligible.

Weyl Anomaly Induced Current in Boundary Quantum Field Theories.

We show that when an external magnetic field parallel to the boundary is applied, the Weyl anomaly gives rises to a new anomalous current in the vicinity of the boundary. The induced current is a magnetization current in origin: the movement of the virtual charges near the boundary give rise to a nonuniform magnetization of the vacuum and hence a magnetization current. Unlike other previously studied anomalous current phenomena such as the chiral magnetic effect or the chiral vortical effect, this induced current does not rely on the presence of a material system and can occur in vacuum. Similar to the Casimir effect, our discovered phenomenon arises from the effect of the boundary on the quantum fluctuations of the vacuum. However this induced current is purely quantum mechanical and has no classical limit. We briefly comment on how this induced current may be observed experimentally.

Momentum Space Topology and Non-Dissipative Currents †

Relativistic heavy ion collisions represent an arena for the probe of various anomalous transport effects. Those effects, in turn, reveal the correspondence between the solid state physics and the high energy physics, which share the common formalism of quantum field theory. It may be shown that for the wide range of field–theoretic models, the response of various nondissipative currents to the external gauge fields is determined by the momentum space topological invariants. Thus, the anomalous transport appears to be related to the investigation of momentum space topology—the approach developed earlier mainly in the condensed matter theory. Within this methodology we analyse systematically the anomalous transport phenomena, which include, in particular, the anomalous quantum Hall effect, the chiral separation effect, the chiral magnetic effect, the chiral vortical effect and the rotational Hall effect.

Chiral vortical effect with finite rotation, temperature, and curvature

We perform an explicit calculation of the axial current at finite rotation and temperature in curved space. We find that finite curvature and mass corrections to the chiral vortical effect satisfy a relation of the chiral gap effect, that is, a fermion mass-shift by a scalar curvature. We also point out that a product term of the angular velocity and the scalar curvature shares the same coefficient as the mixed gravitational chiral anomaly. We discuss possible applications of the curvature induced chiral vortical effect to rotating astrophysical compact objects described by the Kerr metric. Instead of direct calculation we assume that the Chern-Simons current can approximate the physical axial current. We make a proposal that the chiral vortical current from rotating compact objects could provide a novel microscopic mechanism behind the generation of collimated jets.

Chiral Torsional Effect

We propose the new nondissipative transport effect - the appearance of axial current of thermal quasiparticles in the presence of background gravity with torsion. For the non-interacting model of massless Dirac fermions the response of the axial current to torsion is derived. The chiral vortical effect appears to be the particular case of the chiral torsional effect. The proposed effect may be observed in the condensed matter systems with emergent relativistic invariance (Weyl/Dirac semimetals and the $^3$He-A superfluid).

Anatomy of the chiral vortical effect

We consider the system of relativistic rotating fermions in the presence of rotation. The rotation is set up as an enhancement of the angular momentum. In this approach the angular velocity for the angular momentum plays the same role as the chemical potential for density. We calculate the axial current using the direct solutions of the Dirac equation with the MIT bag boundary conditions. Next, we consider the alternative way of the rotation description, in which the local velocity of the substance multiplied by the chemical potential serves as the effective gauge field. In this approach this is possible to relate the axial current of the chiral vortical effect for the massless fermions to the topological invariant in momentum space, which is robust to the introduction of interactions. We compare the results for the axial current obtained using the two above mentioned approaches.