1. 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

2. 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

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

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

5. 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

6. 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

7. ARPES: angle-resolved photoemission spectroscopy
NSLS beamline U13UB.

8. 2D spectral plot of superconducting Bi2Sr2CaCu2O8+d*
*Valla, Johnson, QL et al. Science 285, 2110 (1999)

9. 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

10. 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

11. A Weyl semimetal: TaAs
B. Q. Lv, H. Ding, et al., Phys. Rev. X 5, (2015)
B. Q. Lv, H Ding, et al., Nat. Phys. 11, 724 (2015)
(Institute of Physics, Beijing)
Xu, et al Science (2015)
(Princeton University)
QM2015, Kobe, Japan – Oct. 1, 2015

12. 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

13. 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, (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

14. 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

15. 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, (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

16. 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: [cond-mat.str-el]

17. 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

18. 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: [cond-mat.str-el]

19. 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: [cond-mat.str-el]

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

21. 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:
QM2015, Kobe, Japan – Oct. 1, 2015

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

23. 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

24. Insulator Semimetal Insulator
(Trivial) (Topological)