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Dynamics of Vortices in Chiral Media: The Chiral Propulsion Effect

Yuji Hirono,

1,2

Dmitri E. Kharzeev,

3,4

and Andrey V. Sadofyev

Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea

Department of Physics, POSTECH, Pohang 37673, Korea

Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA

Department of Physics and RIKEN-BNL Research Center, Brookhaven National Laboratory,

Upton, New York 11973-5000, USA

Theoretical Division, MS B283, Los Alamos National Laborator y, Los Alamos, New Mexico 87545, USA

(Received 29 January 2018; published 1 October 2018)

We study the motion of vortex filaments in chiral media and find a semiclassical analog of the anomaly-

induced chiral magnetic effect. The helical solitonic excitations on vortices in a parity-breaking medium are

found to carry additional energy flow along the vortex in the direction dictated by the sign of chirality

imbalance; we call this new transport phenomenon the chiral propulsion effect. The dynamics of vortex

filaments in the parity-breaking background is described by a modified version of the localized induction

equation. We analyze the linear stability of simple vortex solut ions and study the effects of chiral media on

the excitation spectrum and the growth rate of the unstable modes. We also show that, if the equation of

motion of the filament is symmetric under the simultaneous reversal of parity and time, planar-shape

solutions cannot transport energy.

DOI: 10.1103/PhysRevLett.121.142301

Introduction.—The physics of chiral media has attracted

significant attention recently. Remarkably, it is found that

the quantum chiral anomaly [1,2] affects the macroscopic

behavior of chiral media and induces new transport

phenomena, such as the chiral magnetic [3–7] and chiral

vortical effects [8–12] (CME and CVE, respectively). CME

and CVE refer to the generation of electric currents along

an external magnetic field or vorticity in the presence of a

chirality imbalance. The resulting currents are nondissipa-

tive due to the protection by the global topology of the

gauge field. These chiral effects are expected to occur in a

variety of systems: the quark-gluon plasma, Dirac and Weyl

semimetals, primordial electroweak plasma, and cold

atoms. In quark-gluon plasma, the chirality imbalance

can be produced by topological fluctuations of quantum

chromodynamics, or by the combination of electric and

magnetic fields that accompany heavy-ion collisions. The

parallel electric and magnetic fields can also be used to

create the chirality imbalance in condensed matter systems,

see, e.g., Ref. [13]. In addition, CME and CVE lead to a

new class of instabilities in these systems [14–20].

The CME has been observed experimentally in Dirac

[13,21,22] and Weyl semimetals [23–25]. There is an

ongoing search for CME and the local parity violation

[3,4] induced by the topological fluctuations in the quark-

gluon plasma in heavy-ion collisions at Relativistic Heavy-

Ion Collider and Large Hadron Collider; see Ref. [6] for a

review. In particular, the forthcoming isobar run in the

Spring of 2018 at Relativistic Heavy-Ion Collider is

expected to provide a conclusive result on the occurrence

of CME in heavy-ion collisions [26].

Recently, the STAR collaboration reported the exper-

imental observation of Λ hyperon polarization along the

normal to the reaction plane of the heavy-ion collision,

pointing toward the existence of large vorticity in the

produced quark-gluon fluid [27]. The role of vortical

flows in heavy-ion collisions has been discussed, e.g., in

Refs. [28–39]. It is natural to ask how the dynamics of

vortices is influenced by the chiral anomaly.

In this Letter, we analyze the dynamics of vortices in a

fluid with broken parity; the electromagnetic fields are

treated as fully dynamical. We find a new chiral transport

effect—an additional energy flow along the vortex filament

in the direction determined by the sign of chirality

imbalance, the chiral propulsion effect (CPE).

Motions of vortices in chirally imbalanced media.—Let

us consider the motion of a vortex filament in a fluid. The

vorticity concentrated on the vortex sources the velocity

field according to its definition ω ¼ ∇ × v, where v and ω

are fluid velocity and vorticity, respectively. The velocity

field can be found analogously to the magnetic field of a

thin current (Biot-Savart law). Assuming that the vortex

moves on the flow and the contribution to the velocity from

Published by the American Physical Society under the terms of

the Creative Commons Attribution 4.0 International license.

Further distribution of this work must maintain attribution to

the author(s) and the published article’s title, journal citation,

and DOI. Funded by SCOAP

PHYSICAL REVIEW LETTERS 121, 142301 (2018)

0031-9007=18=121(14)=142301(6) 142301-1 Published by the American Physical Society

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