Chiral modes of topological semimetals under magnetic field

Xiao-Xiao Zhang*
Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Nano-Micro Conference, 2017, 1, 01072
Published Online: 31 October 2017 (Abstract)
DOI:10.11605/cp.nmc2017.01072
Corresponding Author. Email: This email address is being protected from spambots. You need JavaScript enabled to view it.

How to Cite

Citation Information: Xiao-Xiao Zhang, Chiral modes of topological semimetals under magnetic field. Nano-Micro Conference, 2017, 1, 01072 doi: 10.11605/cp.nmc2017.01072

History

Received: 03 June 2017, Accepted: 12 June 2017, Published Online: 31 October 2017

Abstract

Topological Dirac/Weyl semimetals, two new quantum phases of matter, attract broad interests from both con- densed matter and particle physicists [1-3]. A Dirac (Weyl) semimetal with degenerate (nondegenerate) linear touch- ings, dubbed as Dirac (Weyl) points, in the electronic band structure is protected by various crystal symmetries (topology) [4-12]. While a Weyl point bears a topological charge in terms of the momentum-space Berry gauge flux, a Dirac point is neutral since it consists of two Weyl points of the opposite topological charge [13]. In addition, the Dirac (Weyl) semimetal exhibits cusps (Fermi arcs) instead of the conventional Fermi ring at the boundary of the Brillouin zone. On the other hand, because of the Landau level formation under an external magnetic field, these band touchings gain to hold massless chiral one-dimensional channels rarely seen outside the discussion of fundamental particles. As a result of the famous chiral anomaly [14-21], the chiral magnetic effect [22-24]is realized in such systems and is observed as the negative magnetoresistance [25-28].

Here, we try to provide a natural but yet missing analysis of the chiral matter, Weyl semimetal, in terms of the powerful framework of Tomonaga-Luttinger liquid, which enables us to examine the correlation and localization effects largely enhanced in this system under a strong magnetic field. We found new features unique to the 1D channels such as the independent critical exponents for the Greens function and the resistivity, which can be directly compared with experiments of realistic materials. The ubiquitous presence of a large number of Weyl points is also taken into account.

Besides, we consider the Dirac semimetal in the form of a nanowire, i.e., new ingredient of confinement geometry is added to this conventional gapless topological semimetal. Once a magnetic field along the nanowire direction is further applied, there will occur a competition between the effects of the confinement and the magnetic field, which strongly affects how the band gap is opened in the system. Expectedly, the system at finite temperature will show distinct transport features as one turns on and gradually increases the external magnetic field.

There has been an increase of interest recently by the micro- or nano-technology community in considering topo- logical materials emerged in the last decade, whose novel topological properties may bring about new possibilities in various applications. Based on these findings, we hope to clarify a few aspects from the viewpoint of either fundamental science or nano-micro engineering.

References

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[24] D. E. Kharzeev, The Chiral Magnetic Effect and anomaly-induced transport. Progress in Particle and Nuclear Physics. 75, 133-151 (2014). doi:10.1016/j.ppnp.2014.01.002
[25] J. Xiong; S. K. Kushwaha; T. Liang; J. W. Krizan; M. Hirschberger; W. Wang; R. J. Cava; N. P. Ong, Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science. 350, 413-416 (2015). doi:10.1126/science.aac6089
[26] Qiang Li; Dmitri E. Kharzeev; Cheng Zhang; Yuan Huang; I. Pletikosić; A. V. Fedorov; R. D. Zhong; J. A. Schneeloch; G. D. Gu; T. Valla, Chiral magnetic effect in ZrTe5. Nature Physics. 12, 550-554 (2016). doi:10.1038/nphys3648
[27] X. Huang; L. Zhao; Y. Long; P. Wang; D. Chen; Z. Yang; H. Liang; M. Xue; H. Weng; Z. Fang; X. Dai; G. Chen, Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs. Physical Review X. 5, 031023 (2015). doi:10.1103/PhysRevX.5.031023
[28] C. Shekhar; A. K. Nayak; Y. Sun; M. Schmidt; M. Nicklas; I. Leermakers; U. Zeitler; Y. Skourski; J. Wosnitza; Z. Liu; Y. Chen; W. Schnelle; H. Borrmann; Y. Grin; C. Felser; B. Yan, Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP. Nature Physics. 11, 645-649 (2015). doi:10.1038/nphys3372

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© The Author(s) 2017

[1] Hermann Weyl, Elektron und Gravitation. I. Zeitschrift für Physik. 56, 330-352 (1929). doi:10.1007/BF01339504
[2] B. Q. Lv; H. M. Weng; B. B. Fu; X. P. Wang; H. Miao; J. Ma; P. Richard; X. C. Huang; L. X. Zhao; G. F. Chen; Z. Fang; X. Dai; T. Qian; H. Ding, Experimental Discovery of Weyl Semimetal TaAs. Physical Review X. 5, 031013 (2015). doi:10.1103/PhysRevX.5.031013
[3] S.-Y. Xu; I. Belopolski; N. Alidoust; M. Neupane; G. Bian; C. Zhang; R. Sankar; G. Chang; Z. Yuan; C.-C. Lee; S.-M. Huang; H. Zheng; J. Ma; D. S. Sanchez; B. Wang; A. Bansil; F. Chou; P. P. Shibayev; H. Lin; S. Jia; M. Z. Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science. 349, 613-617 (2015). doi:10.1126/science.aaa9297
[4] O. Vafek; A. Vishwanath, Dirac Fermions in Solids: From High-Tc Cuprates and Graphene to Topological Insulators and Weyl Semimetals. Annual Review of Condensed Matter Physics. 5, 83-112 (2014). doi:10.1146/annurev-conmatphys-031113-133841
[5] Y. Ren; Z. Qiao; Q. Niu, Topological phases in two-dimensional materials: a review. Reports on Progress in Physics. 79, 066501 (2016). doi:10.1088/0034-4885/79/6/066501
[6] S. Murakami, Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase. New Journal of Physics. 9, 356 (2007). doi:10.1088/1367-2630/9/9/356
[7] X. Wan; A. M. Turner; A. Vishwanath; S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Physical Review B. 83, 205101 (2011). doi:10.1103/PhysRevB.83.205101
[8] Gábor B. Halász; Leon Balents, Time-reversal invariant realization of the Weyl semimetal phase. Physical Review B. 85, 035103 (2012). doi:10.1103/PhysRevB.85.035103
[9] G. Xu; H. Weng; Z. Wang; X. Dai; Z. Fang, Chern Semimetal and the Quantized Anomalous Hall Effect in HgCr2Se4. Physical Review Letters. 107, 186806 (2011). doi:10.1103/PhysRevLett.107.186806
[10] D. Bulmash; C.-X. Liu; X.-L. Qi, Prediction of a Weyl semimetal in Hg1−x−yCdxMnyTe. Physical Review B. 89, 081106 (2014). doi:10.1103/PhysRevB.89.081106
[11] A. A. Burkov; L. Balents, Weyl Semimetal in a Topological Insulator Multilayer. Physical Review Letters. 107, 127205 (2011). doi:10.1103/PhysRevLett.107.127205
[12] A. A. Zyuzin; S. Wu; A. A. Burkov, Weyl semimetal with broken time reversal and inversion symmetries. Physical Review B. 85, 165110 (2012). doi:10.1103/PhysRevB.85.165110
[13] G. E. Volovik, The Universe in a Helium Droplet (International Series of Monographs on Physics), 1st ed. (Oxford University Press, 2009).
[14] S. L. Adler, Axial-Vector Vertex in Spinor Electrodynamics. Physical Review Journals Archive. 177, 2426 (1969). doi:10.1103/PhysRev.177.2426
[15] J. S. Bell; R. Jackiw, A PCAC puzzle: π0→γγ in the σ-model. Il Nuovo Cimento A (1965-1970). 60, 47-61 (1969). doi:10.1007/BF02823296
[16] H. Nielsen; M. Ninomiya, Absence of neutrinos on a lattice: (I). Proof by homotopy theory. Nuclear Physics B. 185, 20-40 (1981). doi:10.1016/0550-3213(81)90361-8
[17] H. B. Nielsen; Masao Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal. Physics Letters B. 130, 389-396 (1983). doi:10.1016/0370-2693(83)91529-0
[18] C.-X. Liu; P. Ye; X.-L. Qi, Chiral gauge field and axial anomaly in a Weyl semimetal. Physical Review B. 87, 235306 (2013). doi:10.1103/PhysRevB.87.235306
[19] P. Hosur; X. Qi, Recent developments in transport phenomena in Weyl semimetals. Comptes Rendus Physique. 14, 857-870 (2013). doi:10.1016/j.crhy.2013.10.010
[20] A. A. Zyuzin; A. A. Burkov, Topological response in Weyl semimetals and the chiral anomaly. Physical Review B. 86, 115133 (2012). doi:10.1103/PhysRevB.86.115133
[21] A. A. Burkov, Chiral anomaly and transport in Weyl metals. Journal of Physics: Condensed Matter. 27, 113201 (2015). doi:10.1088/0953-8984/27/11/113201
[22] K. Fukushima; D. E. Kharzeev; H. J. Warringa, Chiral magnetic effect. Physical Review D. 78, 074033 (2008). doi:10.1103/PhysRevD.78.074033
[23] D. T. Son; B. Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals. Physical Review B. 88, 104412 (2013). doi:10.1103/PhysRevB.88.104412
[24] D. E. Kharzeev, The Chiral Magnetic Effect and anomaly-induced transport. Progress in Particle and Nuclear Physics. 75, 133-151 (2014). doi:10.1016/j.ppnp.2014.01.002
[25] J. Xiong; S. K. Kushwaha; T. Liang; J. W. Krizan; M. Hirschberger; W. Wang; R. J. Cava; N. P. Ong, Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science. 350, 413-416 (2015). doi:10.1126/science.aac6089
[26] Qiang Li; Dmitri E. Kharzeev; Cheng Zhang; Yuan Huang; I. Pletikosić; A. V. Fedorov; R. D. Zhong; J. A. Schneeloch; G. D. Gu; T. Valla, Chiral magnetic effect in ZrTe5. Nature Physics. 12, 550-554 (2016). doi:10.1038/nphys3648
[27] X. Huang; L. Zhao; Y. Long; P. Wang; D. Chen; Z. Yang; H. Liang; M. Xue; H. Weng; Z. Fang; X. Dai; G. Chen, Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs. Physical Review X. 5, 031023 (2015). doi:10.1103/PhysRevX.5.031023
[28] C. Shekhar; A. K. Nayak; Y. Sun; M. Schmidt; M. Nicklas; I. Leermakers; U. Zeitler; Y. Skourski; J. Wosnitza; Z. Liu; Y. Chen; W. Schnelle; H. Borrmann; Y. Grin; C. Felser; B. Yan, Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP. Nature Physics. 11, 645-649 (2015). doi:10.1038/nphys3372

 

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