Chiral Magnetic Effect in Condensed Matters Qiang Li Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory Dmitri E. Kharzeev Department of Physics and RIKEN-BNL Research Center, Brookhaven National Laboratory Department of Physics and Astronomy, Stony Brook University, New York

XII Quark Confinement and the Hadron Spectrum, Thessaloniki, Greece, Aug. 30, 2016 1st London equation (1935): Perfect conductivity  J  n e2     s E  *  t  m  Heinz and Fritz London  Ballistic acceleration of electric current J by the “transient” electric field E.  Dissipationless charge transfer, no resistance Heike Kamerlingh Onnes (Leiden) The BCS Theory (1957) The resistivity of mercury as a function of temperature (26 October 1911) Bardeen, Cooper, Schrieffer, Phys. Rev. 106, 162 ;108, 1175 (1957).

 Paired electrons (boson)  Medium to provide the “glue” for the Cooper pairs  Superconducting condensation Other way to transfer charge without loss?

Chiral magnetic effect (CME): – the generation of electric current by the chirality imbalance between left- and right-handed in a .   J   CME B

K. Fukushima, D. Kharzeev, & H. Warringa, “Chiral magnetic effect” Phys. Rev. D 78, 074033 (2008). D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, Nuclear Physics A 803 (2008)

Impact in science and technology: Dissipationless transmitting and processing information and energy Time reversal symmetry

   t  t J :T -odd; B :T -odd; E :T -even

    2 ne  Ohmic conductivity J   E  J   E;   m* (dissipative)   J  J   n e2    E    E;    s  Superconductivity  *  t t  m  (non-dissipative)

    J   B  J   B Chiral magnetic effect CME CME (non-dissipative) Massless Fermions – odd system (P, CP) electrons, quarks, and neutrinos

Right-handed Left-handed

Chiral magnetic effect and quark-gluon plasma in heavy-ion collisions (RHIC and LHC) Massless Fermions – Parity odd system (P, CP)

Right-handed Left-handed

Chiral quasiparticles in Condensed Matters

3D semimetals with quasi-particles that have a linear dispersion relation have opened a fascinating possibility to study the quantum dynamics of relativistic field theory in condensed matter experiments. Graphene and 2D Dirac Fermions -a single atomic plane of graphite* Novoselov, et al. Science 306, 666–669 (2004).

Geim and Novoselov The Nobel Prize in Physics 2010 Wikipedia.org

• zero effective mass, • High mobility - quantum effects robust and survive even at room temperature • High electrical current, thermal conductivity and stiffness • Impermeable to gases Castro Neto, et al Rev. Mod. Phys. 81, 109 (2009) 3D semimetals with linear dispersion

Weyl semimetal Dirac semimetal (non-degenerated bands) (doubly degenerated bands)

TaAs ZrTe5 NbAs Na3Bi, NbP Cd As TaP 3 2

• The Dirac point can split into two Weyl points either by breaking the crystal inversion symmetry or time-reversal symmetry. • In condensed matter physics, each Weyl point act like a singularity of the Berry curvature in the Brillion Zone – magnetic monopole in k-space A : TaAs

kx (p/a) k -0.2 -0.1 0 0.1 0.2 y 1

0.5

0 kz (p/c’) EB -0.5 (-0.06, 0.47) (0.06, 0.47) -1 0.6 k 0.4 x ky (p/a) 0.2 k = 0.58 p/a z 0.6 high 0.4 ky (p/a) 0.2 low -0.2 -0.1 0 0.1 0.2

kx (p/a) B. Q. Lv, H. Ding, et al., Phys. Rev. X 5, 031013 (2015) B. Q. Lv, H Ding, et al., Nat. Phys. 11, 724 (2015) (Institute of Physics, Beijing)

ARPES: Angle-Resolved PhotoEmission Spectroscopy

Xu, et al Science 7 349 613-617 (2015) (Princeton University) Chiral Magnetic Effect

Quasiparticles in 3D Quark-gluon plasma in Dirac semimetals heavy-ion collisions

 B  E  0

 E Chiral charges in Dirac semimetals

Chiral chemical potential: Density of chiral charge: 3 2    2   5  L  R   5  5 T   5 2 3 3  2  3 v 3v    Rate of chiral charge generaton: 2   e2 ~ d5 e 5    E  B    j5  F F 2 2 4 22c dt 4  c  v

Chiral anomaly Chirality-changing scattering time e2   For t   v   E  B 5 4 22c v

K. Fukushima, D. Kharzeev, and H. Warringa. Phys. Rev. D, 78, 074033 (2008). D. E. Kharzeev. “The chiral magnetic effect and anomaly-induced transport”. Progress in Particle and Nuclear Physics 75, 133 (2014). Chiral Magnetic Effect (CME) in Condensed Matter   3 v3 e2 E  B Chiral chemical potential:    5 4  2 2c  2 v T 2   2 Chiral magnetic current:  e2  2 2 3 i e 3 e v  v i k k ik k JCME  5B J  B B E   E 2 2 CME  8 c  3  2 CME T 2   2

CME conductivity e2 3 e2 v3   zz  v B2  (T) B2 for B//E: CME  8 c  3  2 T 2   2

J  JOhm  JCME  (Ohm CME )E

K. Fukushima, D. Kharzeev, and H. Warringa. Phys. Rev. D, 78, 074033 (2008). D. E. Kharzeev, Progress in Particle and Nuclear Physics 75, 133 (2014). ZrTe5 structure

Hongming Weng, Xi Dai, and Zhong Fang Phys. Rev. X 4, 011002 (2014) 3D Dirac Semimetals: ZrTe5 - Electronic structure by ARPES

Band Inversion

• The states forming the small, hole-like Fermi surface (FS) disperse linearly over a large energy range, indicating a Dirac-like dynamics of carriers

• The velocity, or the slope of dispersion, is very large, va ~ 6.4 eVÅ(~ c/300), vc ~ 4.5 eVÅ Magneto-transport properties of ZrTe5

• Huge positive magnetoresistance when magnetic field is perpendicular to the current (f = 0)

• Large negative magnetoresistance when magnetic field is parallel with the current (f = 90o)

arXiv:1412.6543, Nature Physics (2016) doi:10.1038/nphys3648 Origin of large positive magnetoresistance

• Huge positive magnetoresistance when magnetic field is perpendicular to the current

• Balanced hole–electron ‘resonance’ condition

• Known in high-purity elemental bismuth, a semimetal, and graphite

• Perfect balanced hole-electron condition

as in WTe2 – Nature, doi:10.1038/nature13763 Magneto-transport properties when H//I, q = 0

2  = o +CME = o + a(T)B

2 where o is the zero field conductivity, and a(T) is in unit of S/(cmT )

arXiv:1412.6543 [cond-mat.str-el] Chiral magnetic effect for f = 0o and 18o

2 2 3 zz e 3 e v V 2 2  CME  B  a(T)B 1 D  8 c  3  2 T 2  V   2 

At 20K, o ~ 1.2 mWcm, D ≈ 50 meV,  ~ 9 meV,  ~ 1/300c. arXiv:1412.6543, Nature Physics (2016) doi:10.1038/nphys3648 Chiral magnetic effect in Dirac semimetal Na3Bi

J.Xiong, N. P. Ong et al (Princeton University) arxiv:1503.08179; Science 350:413,2015

19 Chiral magnetic effect in Dirac/Weyl semimetals Dirac semimetals: ZrTe5 - Q. Li, et al (BNL and Stony Brook Univ.) Na3Bi arXiv:1412.6543; Nat. Phys., doi:10.1038/NPHYS3648

Na3Bi - J. Xiong, N. P. Ong et al (Princeton Univ.) arxiv:1503.08179; Science 350:413,2015

Cd3As2- C. Li et al (Peking Univ. China) arxiv:1504.07398; Nat. Commun. 6, 10137 (2015).

Weyl semimetals TaAs - X. Huang et al (IOP, China) arxiv:1503.01304; Phys. Rev. X 5, 031023 TaAs NbAs - X. Yang et al (Zhejiang Univ. China) arxiv:1506.02283 NbP - Z. Wang et al (Zhejiang Univ. China) arxiv:1506.00924 TaP - Shekhar, C. Felser, B. Yang et al (MPI-Dresden) arxiv:1506.06577, Nat. Commun. 7, 11615 (2016).

20 Summary

• Chiral magnetic effect has been observed in condensed matter systems

• 3D Dirac semimetals have opened a fascinating possibility to study the quantum dynamics of relativistic field theory in condensed matter experiments, with potential for important practical applications.

Collaborators C. Zhang, G. Gu, T. Valla (BNL) I. Pletikosic (Princeton University) A. V. Fedorov (LBNL)

From left: T. Valla, DK, QL, G. Gu