1
The chiral magnetic effect
in quark-gluon plasma and condensed matter
D. Kharzeev
Chirality and transport:
classical physics
Chirality and hydrodynamics 240 B.C.
3
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
T-reversal
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
J.-P.Sauvage
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
A(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
18
A
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
19
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
20
spin
momentum
21
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’04
DK, McLerran, Warringa’07 Fukushima, DK, Warringa ‘08
Chiral magnetic conductivity:
discrete symmetries
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P-even T-odd P-odd
P-odd P-odd
T-odd
P-odd effect!
T-even
Non-dissipative current!
(topologically protected)
cf Ohmic
conductivity:
T-odd,
dissipative
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
1/3
CME out of equilibrium:
chiral kinetic theory
DK, M.Stephanov, H.-U.Yee.
arXiv:1612.01674; PRD’17
1/3
CKT:
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
27
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
28
Vector current
Axial current
Magnetic field Vorticity
DK, H.-U. Yee,
arXiv:1012.6026 [hep-th];
PRD
The CME in relativistic hydrodynamics:
The Chiral Magnetic Wave
29
Propagating chiral wave: (if chiral symmetry is restored)
Gapless collective mode is the carrier of CME current in MHD:
CME Chiral separation
Electric
Chiral
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!
Chiral
Electric
Anomalous transport in real time
:axial charge
B:vector charge
31
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
33
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:
H
DK, McLerran, Warringa ‘07
46
Heavy ion collisions as a source of the strongest magnetic fields available in the Laboratory
DK, McLerran, Warringa, Nucl Phys A803(2008)227
47
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?
arXiv:1708.08901
Important data that challenges all existing theoretical models!
Is there a way to get a conclusive answer?
arxiv:1608.00982
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:
46
BNL - Stony Brook - Princeton - Berkeley
arXiv:1412.6543 [cond-mat.str-el]
Nature Phys.
12 (2016) 550
47
arXiv:1412.6543 (December 2014); Nature Physics 12, 550 (2016)
48
Put the crystal in parallel E, B fields – the anomaly generates chiral charge:
and thus the chiral chemical potential:
49
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:
http://scgp.stonybrook.edu/video_portal/video.php?id=2458
Nature Physics 12, 550 (2016)
Negative MR in TaAs
2Y.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
CME:
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;
then
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?
arXiv:1708.08929
Summary
Chirality
Quantum fields
Strings
holography
Fluid dynamics
Nuclear physics Particle physics
Condensed matter
physics
Real-world applications Cosmology
Biophysics
Reviews:
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
