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The chiral magnetic effect


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The chiral magnetic effect

in quark-gluon plasma and condensed matter

D. Kharzeev


Chirality and transport:

classical physics


Chirality and hydrodynamics 240 B.C.


The Archimedes screw


Propeller effect in a fluid

How to rotate the chiral molecule in a fluid?

Use the coupling of

an external electric field to the molecule’s electric dipole moment!

Rotating electric field – rotating molecule

Baranova, Zel’dovich ‘78


D.Schamel et al, JACS 135, 12353 (2013)


D.Schamel et al, JACS 135, 12353 (2013)


E.M.Purcell (1912-1997)

Nobel prize, 1952 (Nuclear Magnetic Resonance)


Stokes equation (“creeping flow”) T-invariance!

Sir G. Stokes (1819-1903)

Geometry of the gauge field on the space of shapes

A.Shapere, F.Wilczek ‘88


Need to break T-invariance to move – chirality!

Left-handed screw



The propulsion matrix

Chiral propellers at low Reynolds number

S.Ayf, I.Cook, DK, to appear

B=20 G B=50 G

Chirality imbalance = transport

0.5 μm


Chirality and vision

Protein-bound retinal molecule as a chiroptical switch:

the mechanism of vision chiral photo-pharmacology

B. Feringa, W. Browne,

“Molecular switches”, 2011


Chiroptical switching of chiral molecules

Need circularly polarized light (CPL), with frequency optimized for inducing the tunnel transition between the enantiomers.

Applications: pharmaceutics, “chiral photomedicine”, optical data storage and processing, …

Review: B.Feringa, J. Org. Chem., 2007, 72 (18), pp 6635–6652



Sir J.F.Stoddart

B.L. Feringa


Chirality and quantum transport


Chiral anomaly

S. Adler ‘69

J. Bell, R. Jackiw ’69

For massless fermions, the axial current

is conserved classically due to the global U


(1) symmetry:

However this conservation law is destroyed by quantum effects


Chiral anomaly

The chiral anomaly does not vanish at finite mass, and mass corrections have been evaluated, see e.g.

A.D. Dolgov, V.I. Zakharov, Nucl. Phys. B27 (1971) 525 R. Armillis et al, JHEP 0912 (2009) 029

Possibility of anomalous transport in systems with a finite gap (strange quarks, semiconductors)?

S. Adler ‘69

J. Bell, R. Jackiw ’69


Chiral anomaly



In classical background fields (E and B), chiral anomaly induces a

collective motion in the Dirac sea

Adler; Bell, Jackiw; Nielsen, Ninomiya; …


Chiral Magnetic Effect

K.Fukushima, DK, H.Warringa, PRD’08;

Review and list of refs: DK, arXiv:1312.3348

Chiral chemical potential is formally

equivalent to a background chiral gauge field:

In this background, and in the presence of B, vector e.m. current is generated:

Compute the current through

The result: Coefficient is fixed by the axial anomaly, no corrections


Absent in Maxwell theory!

The same form as found by Vilenkin’80, but no cancelation since the chiral charge is not conserved Time derivative

of the axion field!


Chirality in 3D:

the Chiral Magnetic Effect

chirality + magnetic field = current






arXiv:1105.0385, PRL


Chiral magnetic effect as a signature of chiral symmetry restoration

V.Braguta et al, arxiv:1704.07132, and to appear

The spontaneous breaking of chiral symmetry does not allow the chiral magnetic current to propagate


DK, McLerran, Warringa’07 Fukushima, DK, Warringa ‘08


Chiral magnetic conductivity:

discrete symmetries


P-even T-odd P-odd

P-odd P-odd


P-odd effect!


Non-dissipative current!

(topologically protected)

cf Ohmic




Effect persists in hydrodynamics!

P – parity

T – time reversal


Dynamical chiral magnetic effect

H.-U. Yee, arXiv:0908.4189, JHEP 0911:085, 2009;

A.Rebhan, A.Schmitt, S.Stricker JHEP 0905, 084 (2009), G.Lifshytz, M.Lippert, arXiv:0904.4772;.A. Gorsky, P. Kopnin, A. Zayakin, arXiv:1003.2293, A.Gynther, K. Landsteiner, F. Pena Benitez, JHEP 1102 (2011) 110; V.

Rubakov, arXiv:1005.1888, C. Hoyos, T. Nishioka, A. O’Bannon, JHEP1110 (2011) 084; …

CME persists at strong coupling - hydrodynamical formulation?

D.K., H. Warringa

Phys Rev D80 (2009) 034028

Strong coupling Weak coupling



CME out of equilibrium:

chiral kinetic theory

DK, M.Stephanov, H.-U.Yee.

arXiv:1612.01674; PRD’17



M. Stephanov, Y. Yin, PRL109(2012)162001;

J.W. Chen, S. Pu, Q. Wang, X.-N.Wang, PRL110(2013)262301;

J.W. Chen, T. Ishii, S. Pu, N. Yamamoto, PRD93(2016)125023; …

AC CME conductivity: why 1/3?

2/3 from Berry phase, 1/3 from energy shift – so

at finite frequency expect 2/3 – what is the missing -1/3?

Magnetization current!


Hydrodynamics and symmetries

• Hydrodynamics: an effective low-energy TOE. States that the response of the fluid to slowly varying

perturbations is completely determined by

conservation laws (energy, momentum, charge, ...)

• Conservation laws are a consequence of symmetries of the underlying theory

• What happens to hydrodynamics when these

symmetries are broken by quantum effects (anomalies of QCD and QED)?

Son, Surowka; Landsteiner, Megias, Pena-Benitez; Sadofyev, Isachenkov; Kalaydzhyan, Kirsch; DK, 26 Yee; Zakharov; Jensen, Loganayagam, Yarom; Neiman, Oz; ….


No entropy production from P-odd anomalous terms


DK and H.-U. Yee, 1105.6360; PRD

Mirror reflection:

entropy decreases ?

Decrease is ruled out by 2nd law of thermodynamics Entropy grows

Allows to compute analytically 13 out of 18 anomalous transport coefficients in 2nd order relativistic hydrodynamics


Systematics of anomalous conductivities


Vector current

Axial current

Magnetic field Vorticity


DK, H.-U. Yee,

arXiv:1012.6026 [hep-th];


The CME in relativistic hydrodynamics:

The Chiral Magnetic Wave


Propagating chiral wave: (if chiral symmetry is restored)

Gapless collective mode is the carrier of CME current in MHD:

CME Chiral separation




The Chiral Magnetic Wave:

oscillations of electric and chiral charges coupled by the chiral anomaly

DK, H.-U. Yee, Phys Rev D’11 30

In strong magnetic field, CMW propagates with the speed of light!




Anomalous transport in real time

:axial charge


:vector charge


Static U(1) magnetic field in z-dir

M. Mace, N. Mueller, S. Schlichting, S. Sharma, arxiv:1704.05887; PRD’17

Chiral Magnetic Wave in real time!


Chiral Magnetohydrodynamics (CMHD)

Y.Hirono, T.Hirano, DK, (Stony Brook – Tokyo), arxiv:1412.0311 (3+1) ideal CMHD (Chiral MagnetoHydroDynamics)

BEST Theory Collaboration (DOE)

Electric charge Chiral charge



B field evolution in transverse plane

CMHD with dynamical MHD magnetic field from ECHO-QGP: Y. Hirono, M. Mace,

G. Inghirami, F. Becattini,L.Del Zanna, DK


Is there a way to observe CME

in nuclear collisions at RHIC and LHC?

Relativistic ions create a strong magnetic field:


DK, McLerran, Warringa ‘07



Heavy ion collisions as a source of the strongest magnetic fields available in the Laboratory

DK, McLerran, Warringa, Nucl Phys A803(2008)227



Heavy ion collisions: the strongest magnetic

field ever achieved in the laboratory




excess of positive charge

excess of negative charge

Electric dipole moment due to chiral imbalance

DK, hep-ph/0406125; Phys.Lett.B633(2006)260

Charge asymmetry w.r.t. reaction plane

as a signature of chirality imbalance


NB: P-even quantity (strength of P-odd fluctuations) – subject to large background contributions

S.Voloshin ‘04


arxiv:1610.00263 October 2, 2016

Background everywhere?

(dAu at RHIC!)

Magnetic field

in pA?



Important data that challenges all existing theoretical models!

Is there a way to get a conclusive answer?



Approved dedicated Spring 2018 CME run at RHIC with

Zr (Z=40), Ru (Z=44) isobars – a clear, “yes or no” answer


The effect of vorticity:

Λ polarization

STAR Coll., Nature 2017

The vorticity has to survive till hadronization.

The difference in

the polarization of Λ and anti-Λ ?

Hint at magnetic field B ~ 0.01 (Mπ )2

at hadronization

e.g. F.Beccatini et al,

arXiv:1610.02506, PRC’17

Vortical susceptibility of QCD matter:

A.Aristova, D.Frenklakh,

A.Gorsky, DK, 1606.05882; JHEP


Chiral fermions in

Dirac & Weyl semimetals


The discovery of Dirac and Weyl semimetals – 3D chiral materials

Z.K.Liu et al., Science 343 p.864 (Feb 21, 2014)


CME in condensed matter:


BNL - Stony Brook - Princeton - Berkeley

arXiv:1412.6543 [cond-mat.str-el]

Nature Phys.

12 (2016) 550



arXiv:1412.6543 (December 2014); Nature Physics 12, 550 (2016)



Put the crystal in parallel E, B fields – the anomaly generates chiral charge:

and thus the chiral chemical potential:



so that there is a chiral magnetic current:

resulting in the quadratic dependence of CME conductivity on B:

adding the Ohmic one – negative magnetoresistance


Qiang Li’s Distinguished CQM lecture at Simons Center, Feb 19, 2016 50

on video:


Nature Physics 12, 550 (2016)


Negative MR in TaAs


Y.Luo et al, 1601.05524

Towards the room temperature CME


Nonlocal chiral transport

C.Zhang et al, Nature Comm.’17 S.Parameswaran, T.Grover,

DOI: 10.1038/ncomms13741 D.Abanin, D.Pesin, A.Vishwanath PRX4, 031035 (2014)


CME as a new type of superconductivity

Fritz and Heinz London

J ~ ⇠ µ 5 B ~

µ 5 ⇠ ~ E ~ B t E ~ || ~ B


London theory of superconductors, ‘35:

for superconducting

current, tunable by magnetic field!

E ~ ⇠ B 2 J ˙~

consider a micro-device of O(μm) size, so that Chirality is conserved;


DK, arXiv:1612.05677


Chiral photonics

Nano Letters, 2017

Response of surface states

grows linearly in B (chiral anomaly)

Rotation of light polarization on

axion domain walls in the Universe?

currents from time-dependent axion fields?






Quantum fields



Fluid dynamics

Nuclear physics Particle physics

Condensed matter


Real-world applications Cosmology




DK, K. Landsteiner, A. Schmitt, H.U.Yee (Eds),

“Strongly interacting matter in magnetic fields”, Springer, 2013; arxiv:1211.6245

DK, “The chiral magnetic effect and anomaly-induced transport”, Prog.Part.Nucl.Phys. 75 (2014) 133; arxiv: 1312.3348

DK, “Topology, magnetic field and strongly interacting matter”, arxiv: 1501.01336; Ann. Rev. Nucl. Part. Science (2015)

DK, J.Liao, S.Voloshin, G.Wang, “Chiral magnetic and vortical effects in high-energy nuclear collisions: A status report” Prog. Part. Nucl.

Phys. 88 (2016) 1



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