Quantum kinetic theory of the chiral anomaly

Sekine, Akihiko; Culcer, Dimitrie; MacDonald, Allan H.

doi:10.1103/physrevb.96.235134

Title: Quantum kinetic theory of the chiral anomaly

Journal Article · Thu Dec 21 00:00:00 EST 2017 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.96.235134· OSTI ID:1511842

Sekine, Akihiko ^[1]; Culcer, Dimitrie ^[2]; MacDonald, Allan H. ^[1]

The Univ. of Texas at Austin, Austin, TX (United States)
The Univ. of New South Wales, Sydney (Australia)

We present a general quantum kinetic theory of low-field magnetotransport in weakly disordered crystals that accounts fully for the interplay between electric-field-induced interband coherence, Bloch-state scattering, and an external magnetic field. The quantum kinetic equation we derive for the Bloch-state density matrix naturally incorporates the momentum-space Berry phase effects whose influence on Bloch-state wave-packet dynamics is normally incorporated into transport theory in an ad hoc manner. The Berry phase correction to the momentum-space density of states in the presence of an external magnetic field implied by semiclassical wave-packet dynamics is captured by our theory as an intrinsic density-matrix response to a magnetic field. We propose a simple and general procedure for expanding the linear response of the Bloch-state density matrix to an electric field in powers of magnetic field. As an illustration, we apply our theory to magnetotransport in Weyl semimetals. Furthermore we show that the chiral anomaly (positive magnetoconductivity quadratic in magnetic field) that appears when separate Fermi surface pockets surround distinct Weyl points survives only when intervalley scattering is very weak compared to intravalley scattering.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-02ER45958; FG03-02ER45958; FG02-ER45958

OSTI ID:: 1511842

Alternate ID(s):: OSTI ID: 1414504

Journal Information:: Physical Review. B, Vol. 96, Issue 23; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 36 works

Citation information provided by
Web of Science

References (73)

Path integral for gauge theories with fermions Fujikawa, Kazuo Physical Review D, Vol. 21, Issue 10 https://doi.org/10.1103/PhysRevD.21.2848	journal	May 1980
Topological insulators and superconductors Qi, Xiao-Liang; Zhang, Shou-Cheng Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1057	journal	October 2011
Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs Huang, Xiaochun; Zhao, Lingxiao; Long, Yujia Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031023	journal	August 2015
Three-dimensional Dirac semimetal and quantum transport in Cd $_{3}$ As $_{2}$ Wang, Zhijun; Weng, Hongming; Wu, Quansheng Physical Review B, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevB.88.125427	journal	September 2013
Giant negative magnetoresistance induced by the chiral anomaly in individual Cd3As2 nanowires Li, Cai-Zhen; Wang, Li-Xian; Liu, Haiwen Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms10137	journal	December 2015
Consequences of a condensed matter realization of Lorentz-violating QED in Weyl semi-metals Grushin, Adolfo G. Physical Review D, Vol. 86, Issue 4 https://doi.org/10.1103/PhysRevD.86.045001	journal	August 2012
Classification of stable three-dimensional Dirac semimetals with nontrivial topology Yang, Bohm-Jung; Nagaosa, Naoto Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5898	journal	September 2014
Magnetotransport phenomena related to the chiral anomaly in Weyl semimetals Spivak, B. Z.; Andreev, A. V. Physical Review B, Vol. 93, Issue 8 https://doi.org/10.1103/PhysRevB.93.085107	journal	February 2016
Experimental observation of Weyl points Lu, L.; Wang, Z.; Ye, D. Science, Vol. 349, Issue 6248 https://doi.org/10.1126/science.aaa9273	journal	July 2015
Dirac Semimetal in Three Dimensions Young, S. M.; Zaheer, S.; Teo, J. C. Y. Physical Review Letters, Vol. 108, Issue 14 https://doi.org/10.1103/PhysRevLett.108.140405	journal	April 2012
New twist for magnetic monopoles MacDonald, Allan; Niu, Qian Physics World, Vol. 17, Issue 1 https://doi.org/10.1088/2058-7058/17/1/24	journal	January 2004
Topological nodal semimetals Burkov, A. A.; Hook, M. D.; Balents, Leon Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235126	journal	December 2011
Topological response in Weyl semimetals and the chiral anomaly Zyuzin, A. A.; Burkov, A. A. Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115133	journal	September 2012
Berry Phase Correction to Electron Density of States in Solids Xiao, Di; Shi, Junren; Niu, Qian Physical Review Letters, Vol. 95, Issue 13 https://doi.org/10.1103/PhysRevLett.95.137204	journal	September 2005
Observation of Weyl nodes in TaAs Lv, B. Q.; Xu, N.; Weng, H. M. Nature Physics, Vol. 11, Issue 9 https://doi.org/10.1038/nphys3426	journal	August 2015
Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids Son, Dam Thanh; Yamamoto, Naoki Physical Review Letters, Vol. 109, Issue 18 https://doi.org/10.1103/PhysRevLett.109.181602	journal	November 2012
Surface-Quantized Anomalous Hall Current and the Magnetoelectric Effect in Magnetically Disordered Topological Insulators Nomura, Kentaro; Nagaosa, Naoto Physical Review Letters, Vol. 106, Issue 16 https://doi.org/10.1103/PhysRevLett.106.166802	journal	April 2011
Electric-field-induced spin resonance in antiferromagnetic insulators: Inverse process of the dynamical chiral magnetic effect Sekine, Akihiko; Chiba, Takahiro Physical Review B, Vol. 93, Issue 22 https://doi.org/10.1103/PhysRevB.93.220403	journal	June 2016
Weyl semimetal phase in the non-centrosymmetric compound TaAs Yang, L. X.; Liu, Z. K.; Sun, Y. Nature Physics, Vol. 11, Issue 9 https://doi.org/10.1038/nphys3425	journal	August 2015
Path-Integral Measure for Gauge-Invariant Fermion Theories Fujikawa, Kazuo Physical Review Letters, Vol. 42, Issue 18 https://doi.org/10.1103/PhysRevLett.42.1195	journal	April 1979
Chiral magnetic effect Fukushima, Kenji; Kharzeev, Dmitri E.; Warringa, Harmen J. Physical Review D, Vol. 78, Issue 7 https://doi.org/10.1103/PhysRevD.78.074033	journal	October 2008
Chiral magnetic conductivity in an interacting lattice model of parity-breaking Weyl semimetal Buividovich, P. V.; Puhr, M.; Valgushev, S. N. Physical Review B, Vol. 92, Issue 20 https://doi.org/10.1103/PhysRevB.92.205122	journal	November 2015
Evidence for the chiral anomaly in the Dirac semimetal Na3Bi Xiong, J.; Kushwaha, S. K.; Liang, T. Science, Vol. 350, Issue 6259 https://doi.org/10.1126/science.aac6089	journal	September 2015
Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP Arnold, Frank; Shekhar, Chandra; Wu, Shu-Chun Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms11615	journal	May 2016
Anomalous Hall effect Nagaosa, Naoto; Sinova, Jairo; Onoda, Shigeki Reviews of Modern Physics, Vol. 82, Issue 2 https://doi.org/10.1103/RevModPhys.82.1539	journal	May 2010
Chiral magnetic effect in a two-band lattice model of Weyl semimetal Chang, Ming-Che; Yang, Min-Fong Physical Review B, Vol. 91, Issue 11 https://doi.org/10.1103/PhysRevB.91.115203	journal	March 2015
Linear response theory of interacting topological insulators Culcer, Dimitrie Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235411	journal	December 2011
Chiral anomaly and transport in Weyl metals Burkov, A. A. Journal of Physics: Condensed Matter, Vol. 27, Issue 11 https://doi.org/10.1088/0953-8984/27/11/113201	journal	February 2015
Quantized Hall Conductance in a Two-Dimensional Periodic Potential Thouless, D. J.; Kohmoto, M.; Nightingale, M. P. Physical Review Letters, Vol. 49, Issue 6 https://doi.org/10.1103/PhysRevLett.49.405	journal	August 1982
Gyrotropic Magnetic Effect and the Magnetic Moment on the Fermi Surface Zhong, Shudan; Moore, Joel E.; Souza, Ivo Physical Review Letters, Vol. 116, Issue 7 https://doi.org/10.1103/PhysRevLett.116.077201	journal	February 2016
Necessary and sufficient condition for longitudinal magnetoresistance Pal, H. K.; Maslov, D. L. Physical Review B, Vol. 81, Issue 21 https://doi.org/10.1103/PhysRevB.81.214438	journal	June 2010
Interband coherence response to electric fields in crystals: Berry-phase contributions and disorder effects Culcer, Dimitrie; Sekine, Akihiko; MacDonald, Allan H. Physical Review B, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevB.96.035106	journal	July 2017
Vertex Corrections to the Anomalous Hall Effect in Spin-Polarized Two-Dimensional Electron Gases with a Rashba Spin-Orbit Interaction Inoue, Jun-ichiro; Kato, Takashi; Ishikawa, Yasuhito Physical Review Letters, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevLett.97.046604	journal	July 2006
Chiral Anomaly and Diffusive Magnetotransport in Weyl Metals Burkov, A. A. Physical Review Letters, Vol. 113, Issue 24 https://doi.org/10.1103/PhysRevLett.113.247203	journal	December 2014
Suppression of the persistent spin Hall current by defect scattering Inoue, Jun-ichiro; Bauer, Gerrit E. W.; Molenkamp, Laurens W. Physical Review B, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevB.70.041303	journal	July 2004
$Z_{2}$ Topological Order and the Quantum Spin Hall Effect Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 14, Article No. 146802 https://doi.org/10.1103/PhysRevLett.95.146802	journal	September 2005
Absence of equilibrium chiral magnetic effect Zubkov, M. A. Physical Review D, Vol. 93, Issue 10 https://doi.org/10.1103/PhysRevD.93.105036	journal	May 2016
Quantum Spin Hall Effect in Graphene Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 22 https://doi.org/10.1103/PhysRevLett.95.226801	journal	November 2005
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Chiral Magnetic Effect and Anomalous Hall Effect in Antiferromagnetic Insulators with Spin-Orbit Coupling Sekine, Akihiko; Nomura, Kentaro Physical Review Letters, Vol. 116, Issue 9 https://doi.org/10.1103/PhysRevLett.116.096401	journal	February 2016
Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2 Neupane, Madhab; Xu, Su-Yang; Sankar, Raman Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms4786	journal	May 2014
Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi Liu, Z. K.; Zhou, B.; Zhang, Y. Science, Vol. 343, Issue 6173 https://doi.org/10.1126/science.1245085	journal	January 2014
Discovery of a Weyl fermion semimetal and topological Fermi arcs Xu, S. -Y.; Belopolski, I.; Alidoust, N. Science, Vol. 349, Issue 6248 https://doi.org/10.1126/science.aaa9297	journal	July 2015
Topological Insulator Materials Ando, Yoichi Journal of the Physical Society of Japan, Vol. 82, Issue 10, Article No. 102001 https://doi.org/10.7566/JPSJ.82.102001	journal	October 2013
Negative longitudinal magnetoresistance in Dirac and Weyl metals Burkov, A. A. Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.245157	journal	June 2015
Dirac semimetal and topological phase transitions in $A_{3}$ Bi ( $A = Na$ , K, Rb) Wang, Zhijun; Sun, Yan; Chen, Xing-Qiu Physical Review B, Vol. 85, Issue 19 https://doi.org/10.1103/PhysRevB.85.195320	journal	May 2012
Generalized Bloch theorem and chiral transport phenomena Yamamoto, Naoki Physical Review D, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevD.92.085011	journal	October 2015
Chiral magnetic effect and natural optical activity in metals with or without Weyl points Ma, Jing; Pesin, D. A. Physical Review B, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevB.92.235205	journal	December 2015
Quantum Spin Hall Effect Bernevig, B. Andrei; Zhang, Shou-Cheng Physical Review Letters, Vol. 96, Issue 10 https://doi.org/10.1103/PhysRevLett.96.106802	journal	March 2006
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane, F. D. M. Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2015	journal	October 1988
Anomalous Hall Coulomb drag of massive Dirac fermions Liu, Hong; Liu, Weizhe Edward; Culcer, Dimitrie Physical Review B, Vol. 95, Issue 20 https://doi.org/10.1103/PhysRevB.95.205435	journal	May 2017
Theory of quantised Hall conductivity in two dimensions Streda, P. Journal of Physics C: Solid State Physics, Vol. 15, Issue 22 https://doi.org/10.1088/0022-3719/15/22/005	journal	August 1982
Chiral anomaly and classical negative magnetoresistance of Weyl metals Son, D. T.; Spivak, B. Z. Physical Review B, Vol. 88, Issue 10 https://doi.org/10.1103/PhysRevB.88.104412	journal	September 2013
Two applications of axion electrodynamics Wilczek, Frank Physical Review Letters, Vol. 58, Issue 18 https://doi.org/10.1103/PhysRevLett.58.1799	journal	May 1987
Experimental Realization of a Three-Dimensional Dirac Semimetal Borisenko, Sergey; Gibson, Quinn; Evtushinsky, Danil Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/PhysRevLett.113.027603	journal	July 2014
Chiral anomaly, charge density waves, and axion strings from Weyl semimetals Wang, Zhong; Zhang, Shou-Cheng Physical Review B, Vol. 87, Issue 16 https://doi.org/10.1103/PhysRevB.87.161107	journal	April 2013
Anomalous Hall response of topological insulators Culcer, Dimitrie; Das Sarma, S. Physical Review B, Vol. 83, Issue 24 https://doi.org/10.1103/PhysRevB.83.245441	journal	June 2011
Chiral magnetic effect in ZrTe5 Li, Qiang; Kharzeev, Dmitri E.; Zhang, Cheng Nature Physics, Vol. 12, Issue 6 https://doi.org/10.1038/nphys3648	journal	February 2016
Suppression of the Kondo resistivity minimum in topological insulators Wang, Jie; Culcer, Dimitrie Physical Review B, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevB.88.125140	journal	September 2013
Weyl Semimetal in the Strong Coulomb Interaction Limit Sekine, Akihiko; Nomura, Kentaro Journal of the Physical Society of Japan, Vol. 83, Issue 9 https://doi.org/10.7566/JPSJ.83.094710	journal	September 2014
Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase New Journal of Physics, Vol. 9, Issue 9 https://doi.org/10.1088/1367-2630/9/9/356	journal	September 2007
Electromagnetic Response of Weyl Semimetals Vazifeh, M. M.; Franz, M. Physical Review Letters, Vol. 111, Issue 2 https://doi.org/10.1103/PhysRevLett.111.027201	journal	July 2013
Negative magnetoresistance in Dirac semimetal Cd3As2 Li, Hui; He, Hongtao; Lu, Hai-Zhou Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10301	journal	January 2016
The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space Fang, Z. Science, Vol. 302, Issue 5642 https://doi.org/10.1126/science.1089408	journal	October 2003
A stable three-dimensional topological Dirac semimetal Cd3As2 Liu, Z. K.; Jiang, J.; Zhou, B. Nature Materials, Vol. 13, Issue 7 https://doi.org/10.1038/nmat3990	journal	May 2014
Berry phase effects on electronic properties Xiao, Di; Chang, Ming-Che; Niu, Qian Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/RevModPhys.82.1959	journal	July 2010
Axionic field theory of $(3 + 1)$ -dimensional Weyl semimetals Goswami, Pallab; Tewari, Sumanta Physical Review B, Vol. 88, Issue 24 https://doi.org/10.1103/PhysRevB.88.245107	journal	December 2013
Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates Wan, Xiangang; Turner, Ari M.; Vishwanath, Ashvin Physical Review B, Vol. 83, Issue 20 https://doi.org/10.1103/PhysRevB.83.205101	journal	May 2011
Apolipoprotein E polymorphism is associated with lower extremity deep venous thrombosis: color-flow Doppler ultrasound evaluation Zhu, ShuangLi; Wang, ZhiGang; Wu, XiaoPing Lipids in Health and Disease, Vol. 13, Issue 1 https://doi.org/10.1186/1476-511x-13-21	journal	January 2014
Linear response theory of interacting topological insulators Culcer, Dimitrie arXiv https://doi.org/10.48550/arxiv.1107.4362	text	January 2011
Suppression of the Kondo Resistivity Minimum in Magnetic Topological Insulators Wang, Jie; Culcer, Dimitrie arXiv https://doi.org/10.48550/arxiv.1308.1952	text	January 2013
Chiral magnetic conductivity in an interacting lattice model of parity-breaking Weyl semimetal Buividovich, P. V.; Puhr, M.; Valgushev, S. N. arXiv https://doi.org/10.48550/arxiv.1505.04582	text	January 2015
Chiral magnetic effect and natural optical activity in (Weyl) metals Ma, Jing; Pesin, D. A. arXiv https://doi.org/10.48550/arxiv.1510.01304	text	January 2015

Cited By (6)

Nonclassical Longitudinal Magnetoresistance in Anisotropic Black Phosphorus Telesio, Francesca; Hemsworth, Nicholas; Dickerson, William physica status solidi (RRL) – Rapid Research Letters, Vol. 14, Issue 2 https://doi.org/10.1002/pssr.201900347	journal	September 2019
Spatially dispersive circular photogalvanic effect in a Weyl semimetal Ji, Zhurun; Liu, Gerui; Addison, Zachariah Nature Materials, Vol. 18, Issue 9 https://doi.org/10.1038/s41563-019-0421-5	journal	July 2019
Large enhancement of conductivity in Weyl semimetals with tilted cones: Pseudorelativity and linear response Rostamzadeh, Saber; Adagideli, İnanç; Goerbig, Mark Oliver Physical Review B, Vol. 100, Issue 7 https://doi.org/10.1103/physrevb.100.075438	journal	August 2019
Berry curvature induced thermopower in type-I and type-II Weyl semimetals Das, Kamal; Agarwal, Amit Physical Review B, Vol. 100, Issue 8 https://doi.org/10.1103/physrevb.100.085406	journal	August 2019
Symmetry and quantum kinetics of the nonlinear Hall effect Nandy, S.; Sodemann, Inti Physical Review B, Vol. 100, Issue 19 https://doi.org/10.1103/physrevb.100.195117	journal	November 2019
Weyl systems: anomalous transport normally explained Morawetz, Klaus The European Physical Journal B, Vol. 92, Issue 8 https://doi.org/10.1140/epjb/e2019-90514-3	journal	August 2019