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Title: Topological quantum properties of chiral crystals

Abstract

Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. In this paper we show that Kramers–Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin–orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers–Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin–orbit coupling carry non-trivial Chern numbers. Kramers–Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.

Authors:
ORCiD logo [1]; ORCiD logo [2];  [3];  [4];  [4]; ORCiD logo [5]; ORCiD logo [6];  [6];  [7]; ORCiD logo [3];  [4];  [8]; ORCiD logo [9]
  1. Princeton Univ., NJ (United States). Dept. of Physics; National Univ. of Singapore (Singapore). Dept of Physics, Centre for Advanced 2D Materials, and Graphene Research Centre; Academia Sinica, Taipei (Taiwan). Inst. of Physics
  2. Princeton Univ., NJ (United States). Dept. of Physics; Stockholm Univ. (Sweden); KTH Royal Inst. of Technology, Stockholm (Sweden); Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy
  3. Univ. of Zurich (Switzerland). Dept. of Physics
  4. Princeton Univ., NJ (United States). Dept. of Physics
  5. National Sun Yat-Sen Univ., Kaoshiung (Taiwan). Dept. of Physics
  6. National Univ. of Singapore (Singapore). Dept of Physics, Centre for Advanced 2D Materials, and Graphene Research Centre
  7. National Cheng Kung Univ., Tainan City (Taiwan). Dept. of Physics
  8. National Univ. of Singapore (Singapore). Dept of Physics, Centre for Advanced 2D Materials, and Graphene Research Centre; Academia Sinica, Taipei (Taiwan). Inst. of Physics
  9. Princeton Univ., NJ (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); Gordon and Betty Moore Foundation; Singapore National Science Foundation; Nordic Institute for Theoretical Physics; Swiss National Science Foundation (SNSF); European Research Council (ERC); Ministry of Science and Technology of China (MOST)
OSTI Identifier:
1638188
Grant/Contract Number:  
AC02-05CH11231; FG-02-05ER46200; GBMF4547; NRF-NRFF2013-03; ERC-DM-321031; SC0016239; ONR-N00014-14-1-0330; 200021-169061; ERC-StG-Neupert-757867-PARATOP; 107-2636-M-006- 004
Resource Type:
Accepted Manuscript
Journal Name:
Nature Materials
Additional Journal Information:
Journal Volume: 17; Journal Issue: 11; Journal ID: ISSN 1476-1122
Publisher:
Springer Nature - Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
condensed-matter physics; electronic properties and materials; materials science; structure of solids and liquids

Citation Formats

Chang, Guoqing, Wieder, Benjamin J., Schindler, Frank, Sanchez, Daniel S., Belopolski, Ilya, Huang, Shin-Ming, Singh, Bahadur, Wu, Di, Chang, Tay-Rong, Neupert, Titus, Xu, Su-Yang, Lin, Hsin, and Hasan, M. Zahid. Topological quantum properties of chiral crystals. United States: N. p., 2018. Web. doi:10.1038/s41563-018-0169-3.
Chang, Guoqing, Wieder, Benjamin J., Schindler, Frank, Sanchez, Daniel S., Belopolski, Ilya, Huang, Shin-Ming, Singh, Bahadur, Wu, Di, Chang, Tay-Rong, Neupert, Titus, Xu, Su-Yang, Lin, Hsin, & Hasan, M. Zahid. Topological quantum properties of chiral crystals. United States. doi:10.1038/s41563-018-0169-3.
Chang, Guoqing, Wieder, Benjamin J., Schindler, Frank, Sanchez, Daniel S., Belopolski, Ilya, Huang, Shin-Ming, Singh, Bahadur, Wu, Di, Chang, Tay-Rong, Neupert, Titus, Xu, Su-Yang, Lin, Hsin, and Hasan, M. Zahid. Mon . "Topological quantum properties of chiral crystals". United States. doi:10.1038/s41563-018-0169-3. https://www.osti.gov/servlets/purl/1638188.
@article{osti_1638188,
title = {Topological quantum properties of chiral crystals},
author = {Chang, Guoqing and Wieder, Benjamin J. and Schindler, Frank and Sanchez, Daniel S. and Belopolski, Ilya and Huang, Shin-Ming and Singh, Bahadur and Wu, Di and Chang, Tay-Rong and Neupert, Titus and Xu, Su-Yang and Lin, Hsin and Hasan, M. Zahid},
abstractNote = {Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. In this paper we show that Kramers–Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin–orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers–Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin–orbit coupling carry non-trivial Chern numbers. Kramers–Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.},
doi = {10.1038/s41563-018-0169-3},
journal = {Nature Materials},
number = 11,
volume = 17,
place = {United States},
year = {2018},
month = {10}
}

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Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals
journal, November 2015

  • Watanabe, Haruki; Po, Hoi Chun; Vishwanath, Ashvin
  • Proceedings of the National Academy of Sciences, Vol. 112, Issue 47
  • DOI: 10.1073/pnas.1514665112

Realizing double Dirac particles in the presence of electronic interactions
journal, September 2017


Type-II Weyl semimetals
journal, November 2015

  • Soluyanov, Alexey A.; Gresch, Dominik; Wang, Zhijun
  • Nature, Vol. 527, Issue 7579
  • DOI: 10.1038/nature15768

Gyrotropic Magnetic Effect and the Magnetic Moment on the Fermi Surface
journal, February 2016


Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996


Current-induced Orbital and Spin Magnetizations in Crystals with Helical Structure
journal, July 2015

  • Yoda, Taiki; Yokoyama, Takehito; Murakami, Shuichi
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep12024

Superconductivity of doped Weyl semimetals: Finite-momentum pairing and electronic analog of the 3 He- A phase
journal, December 2012


Weyl fermions and spin dynamics of metallic ferromagnet SrRuO3
journal, June 2016

  • Itoh, Shinichi; Endoh, Yasuo; Yokoo, Tetsuya
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms11788

Thermodynamically stable magnetic vortex states in magnetic crystals
journal, December 1994


Classification of stable three-dimensional Dirac semimetals with nontrivial topology
journal, September 2014

  • Yang, Bohm-Jung; Nagaosa, Naoto
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms5898

Momentum-space imaging of Cooper pairing in a half-Dirac-gas topological superconductor
journal, November 2014

  • Xu, Su-Yang; Alidoust, Nasser; Belopolski, Ilya
  • Nature Physics, Vol. 10, Issue 12
  • DOI: 10.1038/nphys3139

Experimental observation of Weyl points
journal, July 2015


Electrical Magnetochiral Anisotropy
journal, November 2001


Weyl Semimetal in a Topological Insulator Multilayer
journal, September 2011


Weyl semimetal with broken time reversal and inversion symmetries
journal, April 2012


On Unitary Representations of the Inhomogeneous Lorentz Group
journal, January 1939

  • Wigner, E.
  • The Annals of Mathematics, Vol. 40, Issue 1
  • DOI: 10.2307/1968551

Existence of bulk chiral fermions and crystal symmetry
journal, April 2012


Double Dirac Semimetals in Three Dimensions
journal, May 2016


Dirac Semimetal in Three Dimensions
journal, April 2012


Discovery of a Weyl fermion semimetal and topological Fermi arcs
journal, July 2015


Strong Intrinsic Spin Hall Effect in the TaAs Family of Weyl Semimetals
journal, September 2016


Topological quantum chemistry
journal, July 2017

  • Bradlyn, Barry; Elcoro, L.; Cano, Jennifer
  • Nature, Vol. 547, Issue 7663
  • DOI: 10.1038/nature23268

π Berry phase and Zeeman splitting of Weyl semimetal TaP
journal, January 2016

  • Hu, J.; Liu, J. Y.; Graf, D.
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep18674

Quantized circular photogalvanic effect in Weyl semimetals
journal, July 2017

  • de Juan, Fernando; Grushin, Adolfo G.; Morimoto, Takahiro
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms15995

Emergence of gapped bulk and metallic side walls in the zeroth Landau level in Dirac and Weyl semimetals
journal, November 2017


Bulk spectroscopic measurement of the topological charge of Weyl nodes with resonant x rays
journal, September 2016


Time-reversal-invariant topological superconductivity in doped Weyl semimetals
journal, July 2014


Interacting Weyl Semimetals: Characterization via the Topological Hamiltonian and its Breakdown
journal, September 2014


Chiral anomaly, charge density waves, and axion strings from Weyl semimetals
journal, April 2013


Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
journal, July 2016


Dirac Line Nodes in Inversion-Symmetric Crystals
journal, July 2015


Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi
journal, November 2017


Chiral and Achiral Crystal Structures
journal, April 2003


Multiple Types of Topological Fermions in Transition Metal Silicides
journal, November 2017


Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks
journal, September 2015


Topological materials discovery using electron filling constraints
journal, October 2017

  • Chen, Ru; Po, Hoi Chun; Neaton, Jeffrey B.
  • Nature Physics, Vol. 14, Issue 1
  • DOI: 10.1038/nphys4277

Electronic structure, photovoltage, and photocatalytic hydrogen evolution with p-CuBi 2 O 4 nanocrystals
journal, January 2016

  • Sharma, Geetu; Zhao, Zeqiong; Sarker, Pranab
  • Journal of Materials Chemistry A, Vol. 4, Issue 8
  • DOI: 10.1039/C5TA07040F

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
journal, May 2011


Evidence for the chiral anomaly in the Dirac semimetal Na3Bi
journal, September 2015