Chiral Magnetic Effect in Condensed Matter Systems Qiang Li Condensed Matter Physics & Materials Science Department, BNL In collaboration with Dmitri E. Kharzeev (SBU/BNL), C. Zhang, G. Gu, T. Valla (BNL) I. Pletikosic (Princeton University), A. V. Fedorov (LBNL) QM2015, Kobe, Japan – Oct. 1, 2015

Outline: Quasi-particles in condensed matter systems 2D and 3D Dirac fermions Weyl fermions Graphene and semimetals Chiral magnetic effect in 3D Dirac/Weyl semimetals Summary QM2015, Kobe, Japan – Oct. 1, 2015

Electrons in solids (crystals) A single simple atomic state Fermi Surface of Cu (UF/Phys)

Quasi-particle zoo A. K. Geim, Science 324,1530 (2009)

The Nobel Prize in Physics 2010 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 It is the thinnest known material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have zero effective mass, and can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of magnitude higher than that of copper, shows record thermal conductivity and stiffness, is impermeable to gases, and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation. Vf/c = 1/300 Castro Neto, et al Rev. Mod. Phys. 81, 109 (2009) QM2015, Kobe, Japan – Oct. 1, 2015

Experimental probes to electronic structure of matter Classical ones: magnetoresistance, anomalous skin effect, cyclotron resonance, magneto-acoustic geometric effects, the Shubnikov-de Haas effect,, the de Hass-van Alphen effect. On the momentum distribution: positron annihilation, Compton scattering, etc. Modern ones: angle-resolved photoemission spectroscopy (ARPES), Spectroscopic STM, IR Optical spectroscopy, etc NSLS II BNL-NSLS

ARPES: angle-resolved photoemission spectroscopy NSLS beamline U13UB.

2D spectral plot of superconducting Bi2Sr2CaCu2O8+d* *Valla, Johnson, QL et al. Science 285, 2110 (1999)

3D Dirac Semimetals: ZrTe5 - Electronic structure by ARPES Band Inversion A necessary requirement for observation of the CME is that a material has a 3D Dirac semimetal-like (zero gap), or semiconductor-like (non-zero gap) electronic structure. Figure shows angle-resolved photoemission spectroscopy (ARPES) data from a freshly cleaved (a 􀀀 c plane) ZrTe5 sample. The states forming the small, hole-like Fermi surface (FS) disperse linearly over a large energy range, both along the chain direction (panel (c)) and perpendicular to it (panel (a)), indicating a Dirac-like dynamics of carriers for the in-plane propagation. The velocity, or the slope of dispersion, is very large in both the chain direction,va ' 6:4 eVA(' c=300), and perpendicular to it, vc ' 4:5 eVA. The Dirac point is estimated to be 0:2 eV above the EF . 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 QM2015, Kobe, Japan – Oct. 1, 2015

Fermions (mathematically): Dirac fermions Weyl fermions* Majorana fermions (massive) (massless) (its own antiparticle) Wikipedia.org Wikipedia.org The Standard Model *Hermann Weyl “Elektron und Gravitation“ I. Zeitschrift fur Physik, 56:330–352 (1929) “My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.” - Hermann Weyl (1885 – 1955) A Weyl fermion is one-half of a charged Dirac fermion of a definite chirality QM2015, Kobe, Japan – Oct. 1, 2015

A Weyl semimetal: TaAs 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) Xu, et al Science 7 349 613-617 (2015) (Princeton University) QM2015, Kobe, Japan – Oct. 1, 2015

3D semimetals with linear dispersion Weyl semimetal (non-degenerated bands) Dirac semimetal (doubly degenerated bands) ZrTe5 Na3Bi, Cd3As2 TaAs NbAs NbP TaP 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 QM2015, Kobe, Japan – Oct. 1, 2015

Chiral magnetic effect (CME) – the generation of electric current by the chirality imbalance between left- and right-handed fermions in a magnetic field. D. Kharzeev, L.McLerran, H.Warringa, 2007 K. Fukushima, D. Kharzeev, and H. Warringa. Phys. Rev. D, 78, 074033 (2008). 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. QM2015, Kobe, Japan – Oct. 1, 2015

Chiral Magnetic Effect (CME) in Condensed Matter Adler, Phys. Rev. 177, 2426 (1969) Bell & Jackiw, Nuov Cim 60, 47–61 (1969) Adler-Bell-Jackiw anomaly I At E•B ≠ 0, the particle number for a given chirality is not conserved quantum mechanically, a phenomenon known as the Adler-Bell-Jackiw anomaly* *H.B.Nielsen and Masao Ninomiya, Physics Letters B 130, 389 (1983) QM2015, Kobe, Japan – Oct. 1, 2015

Chiral Magnetic Effect (CME) in Condensed Matter In the quantum field theory of Weyl fermions coupled to electromagnetic gauge field, NL,R, the number of fermion carrying chirality (L, or R) is given by Non-zero chiral chemical potential: CME current: 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). QM2015, Kobe, Japan – Oct. 1, 2015

Magneto-transport properties of ZrTe5 Huge positive magnetoresistance when magnetic field is perpendicular to the current (q = 0) Large negative magnetoresistance when magnetic field is parallel with the current (q = 90o) arXiv:1412.6543 [cond-mat.str-el]

Magneto-transport properties when H//I, q = 0 For clarity, the resistivity curves were shifted by 1.5 mWcm (150 K), 0.9 mWcm (100 K), 0.2 mWcm (70 K), -0.2 mWcm (5 K). Negative magnetoresistance develops at ~ 100 K Small cusps at very low field are due to the weak anti-localization

Magneto-transport properties when H//I, q = 0 s = so +sCME = so + a(T)B2 where so is the zero field conductivity, and a(T) is in unit of S/(cmT2) arXiv:1412.6543 [cond-mat.str-el]

Magneto-transport properties when q = 0 Quadratic field dependence of the magnetoconductance at B//I is a clear indication of the chiral magnetic effect arXiv:1412.6543 [cond-mat.str-el]

CME confirmed in several recent observations Dirac semimetals: ZrTe5, Na3Bi, Cd3As2 Weyl semimetals: TaAs, NbAs, NbP, TaP TaAs: X.Huang et al (Beijing) arxiv:1503.01304, PRX TaP: Shekhar et al (Dresden) arxiv:1506.06577v1 Na3Bi: J.Xiong et al (Princeton) arxiv:1503.08179, Science 20

Implications Weyl materials are direct 3-D electronic analogs of graphene Weyl fermions are massless, theoretically travel 1000x faster than ordinary semiconductors, and at least twice as fast as graphence New type of quantum computing Weyl fermions are less prone to interacting with their environment, due to chirality conservation Lossless Chiral magnetic current (≠ superconductors) Chiral magnetic waves, plasmons, and THZ irradiation D. Kkarzeev, R. Pisarski, H.-U. Yee, arxiv: 1412.6106 QM2015, Kobe, Japan – Oct. 1, 2015

Plasmons, THZ Irradiation (T-Ray) in Dirac semimetals 100 cm-1 ~ 3 THZ D. Kkarzeev, R. Pisarski, H.-U. Yee, arxiv: 1412.6106 QM2015, Kobe, Japan – Oct. 1, 2015

Summary Chiral magnetic field (CME) has been observed in condensed matter systems 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, with potential for important practical applications. QM2015, Kobe, Japan – Oct. 1, 2015

Insulator Semimetal Insulator (Trivial) (Topological)