Dynamics of Vortices in Chiral Media: The Chiral Propulsion Effect
Yuji Hirono,
1,2
Dmitri E. Kharzeev,
3,4
and Andrey V. Sadofyev
5
1
Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea
2
Department of Physics, POSTECH, Pohang 37673, Korea
3
Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
4
Department of Physics and RIKEN-BNL Research Center, Brookhaven National Laboratory,
Upton, New York 11973-5000, USA
5
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
3
.
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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