Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 50 (2017)

Chiral magnetic superconductivity†
D.E. Kharzeev∗1∗2∗3
Materials with charged chiral quasiparticles in external parallel electric and magnetic ﬁelds can support anelectric current that grows linearly in time, corresponding to diverging DC conductivity. From experimental
viewpoint, this “Chiral Magnetic Superconductivity”(CMS) is thus analogous to conventional superconductivity. However the underlying physics is entirely different – the CMS does not require a condensate ofCooper pairs breaking the gauge degeneracy, and isthus not accompanied by Meissner eﬀect. Instead, itowes its existence to the (temperature-independent)
quantum chiral anomaly and the conservation of chirality. As a result, this phenomenon can be expected
to survive to much higher temperatures. Even though
the chirality of quasiparticles is not strictly conservedin real materials, the chiral magnetic superconductivity should still exhibit itself in AC measurements at
frequencies larger than the chirality-ﬂipping rate, andin microstructures of Dirac and Weyl semimetals withthickness below the mean chirality-ﬂipping length thatis about 1 − 100 μm. In nuclear physics, the CMS
should contribute to the charge-dependent elliptic ﬂow
in heavy ion collisions.
Let us start with a brief recap of “conventional” superconductivity. Instead of microscopic BCS theory
introducing the condensate of Cooper pairs, we willbase our discussion on the approach proposed in 1935
by Fritz and Heinz London. The London equations
describe electromagnetic response of a superconductor
and can be derived from the following bold assumption
about the proportionality between the electric current
J and the vector gauge potential A:
J = −μ2 A,(1)where a phenomenological constant μ is related to thedensity of superconducting carriers ns , electron mass
m and electric charge e by μ = (e2 ns /m)1/2 .
In Coulomb gauge, the electric ﬁeld is E = −Ȧ andthe magnetic ﬁeld is B = ∇ × A; therefore, the assumption (1) yields the following two equations of superconductor electrodynamics:
J̇ = μ2 E,(2)and∇ × J = −μ2 B.

(3)The ﬁrst of these equations (2) tells us that a constant†Condensed from the article in arXiv:1612.05677∗1RIKENNishinaCenter∗2 Department of Physics and Astronomy, Stony Brook University, Stony Brook∗3 Department of Physics, Brookhaven National Laboratory,
Upton- 127 -

external electric ﬁeld E generates inside a superconductor a transient state with an electric current thatgrows linearly in time. Once the electric ﬁeld is turnedoﬀ (or screened away), Eq. (2) tells us that the current
J is not allowed to decay and should persist – this issuperconductivity.
To make an analogy with superconductivity, let us
consider a chiral material (i.e. a material that hosts
massless charged chiral fermions, such as a Dirac or
Weyl semimetal, or a quark-gluon plasma) in external parallel magnetic and electric ﬁelds. First, let us
assume that the chirality of fermions is strictly conserved. The chiral anomaly of quantum electrodynamics then dictates that the electric and magnetic
ﬁelds generate the chiral charge density ρ5 with therate given bydρ5e2=E · B,dt
4π 2 h̄2 c(4)and the chiral charge density grows linearly in time:ρ5 =e2E · B t.
4π 2 h̄2 c(5)Let us now relate the density of the chiral charge ρ5and the chiral chemical potential μ5 by introducingχ ≡ ∂ρ5 /∂μ5 , so that ρ5 = χμ5 + ... and μ5  χ−1 ρ5for small μ5 ; note that at late times when μ5 grows
larger than other scales in the system, this relation
will eventually be violated.
For E||B we now get
J=e2e4μB=
χ−1 B2 E t ≡ μ2CME E t.(6)52π 28π 4 h̄2 cTaking the time derivative on both sides, we getJ̇ = μ2CME E,(7)which is completely analogous to the corresponding expression for superconductivity (2)! We thus see thatthe CME1,2) in an ideal chiral material can be viewed
as a new type of superconductivity – we will call it Chiral Magnetic Superconductivity (CMS). In particular,
if the electric ﬁeld is switched oﬀ, the CME current
according to (7) persists. In real experiments, the current will eventually decay, but on a time scale set by
the chirality-ﬂipping transitions that is much longer
than a typical transport time.
References
1) K. Fukushima, D. E. Kharzeev and H. J. Warringa,Phys. Rev. D 78, 074033 (2008) [arXiv:0808.3382 [hepph]].
2) D. E. Kharzeev, Prog. Part. Nucl. Phys. 75, 133 (2014)[arXiv:1312.3348 [hep-ph]].