Physics Letters B 776 (2018) 270–277
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Electrodynamics of dual superconducting chiral medium
Yang Li
a,b,∗
, Kirill Tuchin
a
a
Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
b
Department of Physics, College of William & Mary, Williamsburg, VA 23187, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
4 September 2017
Received
in revised form 26 November 2017
Accepted
26 November 2017
Available
online xxxx
Editor:
J.-P. Blaizot
We study the electrodynamics of the chiral medium with electric and magnetic charges using the
effective Maxwell–Chern–Simons theory extended to include the magnetic current. The exchange of
helicity between the chiral medium and the magnetic field, known as the inverse cascade, is controlled by
the chiral anomaly equation. In the presence of the magnetic current, the magnetic helicity is dissipated,
so that the inverse cascade stops when the magnetic helicity vanishes while the chiral conductivity
reaches a non-vanishing stationary value satisfying σ
2
χ
< 4σ
e
σ
m
, where σ
e
, σ
m
and σ
χ
are the electric,
magnetic and chiral conductivities respectively. We argue that this state is superconducting and exhibits
the Meissner effect for both electric and magnetic fields. Moreover, this state is stable with respect to
small magnetic helicity fluctuations; the magnetic helicity becomes unstable only when the inequality
mentioned above is violated.
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Classical electromagnetic field in a medium with chiral anomaly
is described by a system of Maxwell equations and the chi-
ral
anomaly equation [1,2] known as the Maxwell–Chern–Simons
(MCS) theory [3–6]. The chiral anomaly equation controls the ex-
change
of helicity between the field and medium such that the
total helicity is conserved. The resulting non-trivial evolution of
the magnetic field topology has been a subject of recent inter-
est
[7–18] motivated by phenomenological applications in nuclear
physics, condensed matter physics and cosmology [19].
A
distinctive feature of the MCS theory is the emergence of the
soft magnetic field modes exponentially growing in time [7,8,14,15,
19–28].
These unstable modes transfer helicity from the medium
to the field in a process known as the inverse cascade [8,29]. Even-
tually,
however, the helicity conservation puts a cap on the inverse
cascade [30,31].
It
has been argued in [32–36] that magnetic monopoles play
an important role in quark–gluon plasma dynamics. Magnetic
monopoles also often appear in cosmological models [37] and even
in condensed matter physics [38]. This motivates us to consider the
MCS theory with dynamical magnetic monopoles (MCSm). That the
magnetic monopoles are expected to have non-trivial effects on the
*
Corresponding author.
E-mail
address: yli48@wm.edu (Y. Li).
magnetic field can be seen from the fact that the dual transforma-
tion
generates in the Lagrangian the same CP-odd term as chiral
anomaly. In particular, the magnetic current, while being energy
non-dissipative, causes dissipation of the total helicity. The main
goal of this paper is to uncover the main features of the chiral
magnetic dynamics with magnetic monopoles.
The
paper is organized as follows. In Sec. 2 we formulate the
equations of the MCSm theory and analyze their main properties.
Our main assumption is the linear medium response that is char-
acterized
by the electric and magnetic conductivities σ
e
and σ
m
.
We observe the emergence of the superconducting phase when
σ
2
χ
< 4σ
e
σ
m
and formulate the corresponding London equations
(12), (13) in Sec. 2.2. In Sec. 2.3 we analyze the late-time dynamics
of the MCSm system, in particular, its evolution towards a station-
ary
state. We argue that the magnetic helicity must exponentially
decay due to the helicity dissipating magnetic current. The chiral
conductivity σ
χ
also decays owing to the inverse cascade as men-
tioned
above. However, in the presence of the magnetic current,
the inverse cascade may be terminated before the chiral conduc-
tivity
turns zero. Therefore, the chiral conductivity approaches a
finite stationary value σ
∞
while the magnetic helicity is com-
pletely
dissipated. In Sec. 3 we investigate the dispersion relation
of the magnetic field modes and point out the conditions under
which the magnetic field (and magnetic helicity) is unstable. In
our context, the term “instability” means that a small fluctuation
of the field triggers its exponential growth, even though eventually
it decays as a result of the magnetic helicity non-conservation. We
https://doi.org/10.1016/j.physletb.2017.11.063
0370-2693/
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.