Chiral Magnetic Effect in Condensed Matter Systems

Qiang LiCondensed Matter Physics & Materials Science Department, BNL

QM2015, Kobe, Japan – Oct. 1, 2015

In collaboration with

Dmitri E. Kharzeev (SBU/BNL), C. Zhang, G. Gu, T. Valla (BNL)I. Pletikosic (Princeton University), A. V. Fedorov (LBNL)

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)

Fermi Surface of Cu (UF/Phys)A single simple atomic state

Quasi-particle zoo

A. K. Geim, Science 324,1530 (2009)

Graphene and 2D Dirac Fermions

- a single atomic plane of graphite*Novoselov, et al. Science 306, 666–669 (2004).

QM2015, Kobe, Japan – Oct. 1, 2015

Castro Neto, et al Rev. Mod. Phys. 81, 109 (2009)

• zero effective mass, • High mobility - quantum effects robust

and survive even at room temperature• High electrical current, thermal

conductivity and stiffness• Impermeable to gases

Geim and NovoselovThe Nobel Prize in Physics 2010

Wikipedia.org

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

BNL-NSLS

NSLS II

ARPES: angle-resolved photoemission spectroscopy

OKin EeE

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

QM2015, Kobe, Japan – Oct. 1, 2015

• 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

Band Inversion

Fermions (mathematically):

Dirac fermions Weyl fermions* Majorana fermions (massive) (massless) (its own antiparticle)

QM2015, Kobe, Japan – Oct. 1, 2015

The Standard Model Wikipedia.org Wikipedia.org

*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

A Weyl semimetal: TaAs

QM2015, Kobe, Japan – Oct. 1, 2015

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

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)

3D semimetals with linear dispersion

QM2015, Kobe, Japan – Oct. 1, 2015

Weyl semimetal (non-degenerated bands)

Dirac semimetal (doubly degenerated bands)

• 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

ZrTe5

Na3Bi,

Cd3As2

TaAsNbAsNbPTaP

Chiral magnetic effect (CME)

QM2015, Kobe, Japan – Oct. 1, 2015

– the generation of electric current by the chirality imbalance between left- and right-handed fermions in a magnetic field.

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.

D. Kharzeev, L.McLerran, H.Warringa, 2007K. Fukushima, D. Kharzeev, and H. Warringa. Phys. Rev. D, 78, 074033 (2008).

Adler-Bell-Jackiw anomaly

QM2015, Kobe, Japan – Oct. 1, 2015

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*

Adler, Phys. Rev. 177, 2426 (1969) Bell & Jackiw, Nuov Cim 60, 47–61 (1969)

*H.B.Nielsen and Masao Ninomiya, Physics Letters B 130, 389 (1983)

Chiral Magnetic Effect (CME) in Condensed Matter

QM2015, Kobe, Japan – Oct. 1, 2015

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

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).

v

RLRL NBE

c

e

t

dN

,

22

2,

4

vRL BEc

eN

22

2

, 4

vRL BE

~

Be

JCME

2

2

2 2~ ; BEJ zz

CMEkik

CMEiCME

Non-zero chiral chemical potential:

CME current:

Chiral Magnetic Effect (CME) in Condensed Matter

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

• Negative magnetoresistance develops at ~ 100 K

• Small cusps at very low field are due to the weak anti-localization

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).

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 H//I, q = 0

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]

20

TaAs: X.Huang et al (Beijing) arxiv:1503.01304, PRX

Na3Bi: J.Xiong et al (Princeton) arxiv:1503.08179, Science

CME confirmed in several recent observations

Dirac semimetals:

ZrTe5, Na3Bi, Cd3As2

Weyl semimetals:

TaAs, NbAs, NbP, TaP

TaP: Shekhar et al (Dresden) arxiv:1506.06577v1

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

QM2015, Kobe, Japan – Oct. 1, 2015

D. Kkarzeev, R. Pisarski, H.-U. Yee, arxiv: 1412.6106

Plasmons, THZ Irradiation (T-Ray) in Dirac semimetals

QM2015, Kobe, Japan – Oct. 1, 2015

D. Kkarzeev, R. Pisarski, H.-U. Yee, arxiv: 1412.6106100 cm-1 ~ 3 THZ

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)