Weyl, Dirac and high-fold chiral fermions in topological quantum matter

Hasan, M. Zahid; Chang, Guoqing; Belopolski, Ilya; Bian, Guang; Xu, Su-Yang; Yin, Jia-Xin

doi:10.1038/s41578-021-00301-3

Title: Weyl, Dirac and high-fold chiral fermions in topological quantum matter

Abstract

Quantum materials hosting Weyl fermions have opened a new era of research in condensed matter physics. First proposed in 1929 in the context of particle physics, Weyl fermions have yet to be observed as elementary particles. In 2015, Weyl fermions were detected as collective electronic excitations in the strong spin–orbit coupled material tantalum arsenide, TaAs. This discovery was followed by a flurry of experimental and theoretical explorations of Weyl phenomena in materials. Weyl materials naturally lend themselves to the exploration of the topological index associated with Weyl fermions and their divergent Berry curvature field, as well as the topological bulk–boundary correspondence, giving rise to protected conducting surface states. Here, we review the broader class of Weyl topological phenomena in materials, starting with the observation of emergent Weyl fermions in the bulk and Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss several exotic optical and magnetic responses observed in these materials, as well as progress in developing related chiral materials. We discuss the conceptual development of high-fold chiral fermions, which generalize Weyl fermions, and we review the observation of high-fold chiral fermion phases by taking the rhodium silicide, RhSi, family ofmore »« less

Authors:

^[1];

^[2]; Belopolski, Ilya ^[3]; Bian, Guang ^[4];

^[5];

^[3]

Princeton Univ., NJ (United States). Lab. for Topological Quantum Matter and Advanced Spectroscopy (B7); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Princeton Univ., NJ (United States). Princeton Institute for Science and Technology of Materials
Princeton Univ., NJ (United States). Lab. for Topological Quantum Matter and Advanced Spectroscopy (B7); Nanyang Technological Univ. (Singapore)
Princeton Univ., NJ (United States). Lab. for Topological Quantum Matter and Advanced Spectroscopy (B7)
Princeton Univ., NJ (United States). Lab. for Topological Quantum Matter and Advanced Spectroscopy (B7); Univ. of Missouri, Columbia, MO (United States)
Princeton Univ., NJ (United States). Lab. for Topological Quantum Matter and Advanced Spectroscopy (B7); Harvard Univ., Cambridge, MA (United States)

Publication Date:: Mon Apr 26 00:00:00 EDT 2021

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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

OSTI Identifier:: 1839934

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Nature Reviews. Materials

Additional Journal Information:: Journal Volume: 6; Journal Issue: 9; Journal ID: ISSN 2058-8437

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Condensed-matter physics; Electronic properties and materials; Magnetic properties and materials; Topological insulators; Topological matter

Citation Formats


                    Hasan, M. Zahid, Chang, Guoqing, Belopolski, Ilya, Bian, Guang, Xu, Su-Yang, and Yin, Jia-Xin. Weyl, Dirac and high-fold chiral fermions in topological quantum matter.  United States: N. p., 2021. 
Web.  doi:10.1038/s41578-021-00301-3.

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                    Hasan, M. Zahid, Chang, Guoqing, Belopolski, Ilya, Bian, Guang, Xu, Su-Yang, & Yin, Jia-Xin. Weyl, Dirac and high-fold chiral fermions in topological quantum matter.  United States.  https://doi.org/10.1038/s41578-021-00301-3

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                    Hasan, M. Zahid, Chang, Guoqing, Belopolski, Ilya, Bian, Guang, Xu, Su-Yang, and Yin, Jia-Xin. Mon .  
"Weyl, Dirac and high-fold chiral fermions in topological quantum matter".  United States.  https://doi.org/10.1038/s41578-021-00301-3.  https://www.osti.gov/servlets/purl/1839934.

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@article{osti_1839934,

  title        = {Weyl, Dirac and high-fold chiral fermions in topological quantum matter},

  author       = {Hasan, M. Zahid and Chang, Guoqing and Belopolski, Ilya and Bian, Guang and Xu, Su-Yang and Yin, Jia-Xin},

  abstractNote = {Quantum materials hosting Weyl fermions have opened a new era of research in condensed matter physics. First proposed in 1929 in the context of particle physics, Weyl fermions have yet to be observed as elementary particles. In 2015, Weyl fermions were detected as collective electronic excitations in the strong spin–orbit coupled material tantalum arsenide, TaAs. This discovery was followed by a flurry of experimental and theoretical explorations of Weyl phenomena in materials. Weyl materials naturally lend themselves to the exploration of the topological index associated with Weyl fermions and their divergent Berry curvature field, as well as the topological bulk–boundary correspondence, giving rise to protected conducting surface states. Here, we review the broader class of Weyl topological phenomena in materials, starting with the observation of emergent Weyl fermions in the bulk and Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss several exotic optical and magnetic responses observed in these materials, as well as progress in developing related chiral materials. We discuss the conceptual development of high-fold chiral fermions, which generalize Weyl fermions, and we review the observation of high-fold chiral fermion phases by taking the rhodium silicide, RhSi, family of crystals as a prime example. Lastly, we discuss recent advances in Weyl line phases in magnetic topological materials. With this Review, we aim to provide an introduction to the basic concepts underlying Weyl physics in condensed matter, and to representative materials and their electronic structures and topology as revealed by spectroscopic studies. Finally, we hope this work serves as a guide for future theoretical and experimental explorations of chiral fermions and related topological quantum systems with potentially enhanced functionalities.},

  doi          = {10.1038/s41578-021-00301-3},

  journal      = {Nature Reviews. Materials},

  number       = 9,

  volume       = 6,

  place        = {United States},

  year         = {Mon Apr 26 00:00:00 EDT 2021},

  month        = {Mon Apr 26 00:00:00 EDT 2021}

}

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Title: Weyl, Dirac and high-fold chiral fermions in topological quantum matter

Abstract

Citation Formats

Evidence for magnetic Weyl fermions in a correlated metal journal, September 2017

Extremely high magnetoresistance and conductivity in the type-II Weyl semimetals WP2 and MoP2 journal, November 2017

Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions journal, September 2018

Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal journal, July 2018

Nonlinear photoresponse of type-II Weyl semimetals journal, March 2019

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Experimental observation of Weyl points journal, July 2015

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A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases journal, March 2017

Enhanced anomalous Hall effect in the magnetic topological semimetal Co 3 Sn 2 − x In x S 2 journal, March 2020

Topological Nodal Cooper Pairing in Doped Weyl Metals journal, February 2018

Topological nodal semimetals journal, December 2011

Transport of Topological Semimetals journal, July 2019

Drumhead surface states and topological nodal-line fermions in TlTaSe 2 journal, March 2016

Helicity-dependent photocurrents in the chiral Weyl semimetal RhSi journal, July 2020

The electronic properties of graphene journal, January 2009

Topological electronic structure and Weyl semimetal in the TlBiSe 2 class of semiconductors journal, September 2012

Observation of Weyl nodes in TaAs journal, August 2015

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Weyl semimetal phase in the non-centrosymmetric compound TaAs journal, August 2015

Discovery of Weyl Fermion Semimetals and Topological Fermi Arc States journal, March 2017

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

Observation of topological nodal fermion semimetal phase in ZrSiS journal, May 2016

On the search for the chiral anomaly in Weyl semimetals: the negative longitudinal magnetoresistance journal, August 2016

Topological semimetals with helicoid surface states journal, June 2016

Catalogue of topological electronic materials journal, February 2019

TaIrTe 4 : A ternary type-II Weyl semimetal journal, May 2016

Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet journal, September 2018

Photocurrents in Weyl semimetals journal, January 2017

Magnetic Weyl semimetal phase in a Kagomé crystal journal, September 2019

Fermi arc electronic structure and Chern numbers in the type-II Weyl semimetal candidate Mo x W 1 − x Te 2 journal, August 2016

Stable Weyl points, trivial surface states, and particle-hole compensation in WP 2 journal, May 2018

Nodal-chain metals journal, August 2016

Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal journal, March 2019

Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature journal, October 2015

Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2 journal, October 2016

Topological nodal-line fermions in spin-orbit metal PbTaSe2 journal, February 2016

Elektron und Gravitation. I journal, May 1929

Discovery of Lorentz-violating type II Weyl fermions in LaAlGe journal, June 2017

Topological negative refraction of surface acoustic waves in a Weyl phononic crystal journal, August 2018

Quasiparticle interference and nonsymmorphic effect on a floating band surface state of ZrSiSe journal, October 2018

Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal journal, July 2018

Zero‐Field Nernst Effect in a Ferromagnetic Kagome‐Lattice Weyl‐Semimetal Co 3 Sn 2 S 2 journal, April 2019

Weyl semimetals from noncentrosymmetric topological insulators journal, October 2014

Friedel oscillations due to Fermi arcs in Weyl semimetals journal, November 2012

Chiral magnetic effect and natural optical activity in metals with or without Weyl points journal, December 2015

Edge conduction in monolayer WTe2 journal, April 2017

Chiral topological semimetal with multifold band crossings and long Fermi arcs journal, May 2019

Observation of three-component fermions in the topological semimetal molybdenum phosphide journal, June 2017

Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry journal, June 2012

Topological Materials: Quantum Anomalous Hall System journal, March 2018

Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi journal, February 2019

A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class journal, June 2015

Topological semimetals journal, October 2016

Magnetotransport properties of the type-II Weyl semimetal candidate Ta 3 S 2 journal, November 2016

Three-component fermions with surface Fermi arcs in tungsten carbide journal, January 2018

Weyl semimetals, Fermi arcs and chiral anomalies journal, October 2016

Magnetotransport and de Haas–van Alphen measurements in the type-II Weyl semimetal TaIrTe 4 journal, October 2016

Dirac versus Weyl Fermions in Topological Insulators: Adler-Bell-Jackiw Anomaly in Transport Phenomena journal, December 2013

Ultraquantum magnetoresistance in the Kramers-Weyl semimetal candidate β − Ag 2 Se journal, October 2017

Large, non-saturating magnetoresistance in WTe2 journal, September 2014

Topological semimetals predicted from first-principles calculations journal, June 2016

Observation of Fermi arc surface states in a topological metal journal, December 2014

A strongly robust type II Weyl fermion semimetal state in Ta 3 S 2 journal, June 2016

Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2 journal, December 2016

Topological chiral crystals with helicoid-arc quantum states journal, March 2019

Massive Dirac fermions in a ferromagnetic kagome metal journal, March 2018

Superconductivity in Weyl metals journal, July 2015

Topological semimetals carrying arbitrary Hopf numbers: Fermi surface topologies of a Hopf link, Solomon's knot, trefoil knot, and other linked nodal varieties journal, July 2017

Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2 journal, September 2016

Double-Weyl Phonons in Transition-Metal Monosilicides journal, January 2018

Experimental discovery of a topological Weyl semimetal state in TaP journal, November 2015

Dirac Fermions in Solids: From High-T c Cuprates and Graphene to Topological Insulators and Weyl Semimetals journal, March 2014

Topological Hopf and Chain Link Semimetal States and Their Application to Co 2 Mn G a journal, October 2017

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials journal, November 2015

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

Evidence for magnetic Weyl fermions in a correlated metal
journal, September 2017

Extremely high magnetoresistance and conductivity in the type-II Weyl semimetals WP2 and MoP2
journal, November 2017

Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions
journal, September 2018

Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal
journal, July 2018

Nonlinear photoresponse of type-II Weyl semimetals
journal, March 2019

Topological Materials: Weyl Semimetals
journal, March 2017

Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide
journal, August 2015

Experimental observation of Weyl points
journal, July 2015

Observation of unconventional chiral fermions with long Fermi arcs in CoSi
journal, March 2019

A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases
journal, March 2017

Enhanced anomalous Hall effect in the magnetic topological semimetal $Co_{3} {Sn}_{2 - x} {In}_{x} S_{2}$
journal, March 2020

Topological Nodal Cooper Pairing in Doped Weyl Metals
journal, February 2018

Topological nodal semimetals
journal, December 2011

Transport of Topological Semimetals
journal, July 2019

Drumhead surface states and topological nodal-line fermions in ${TlTaSe}_{2}$
journal, March 2016

Helicity-dependent photocurrents in the chiral Weyl semimetal RhSi
journal, July 2020

The electronic properties of graphene
journal, January 2009

Topological electronic structure and Weyl semimetal in the TlBiSe $_{2}$ class of semiconductors
journal, September 2012

Observation of Weyl nodes in TaAs
journal, August 2015

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

Weyl semimetal phase in the non-centrosymmetric compound TaAs
journal, August 2015

Discovery of Weyl Fermion Semimetals and Topological Fermi Arc States
journal, March 2017

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

Observation of topological nodal fermion semimetal phase in ZrSiS
journal, May 2016

On the search for the chiral anomaly in Weyl semimetals: the negative longitudinal magnetoresistance
journal, August 2016

Topological semimetals with helicoid surface states
journal, June 2016

Catalogue of topological electronic materials
journal, February 2019

${TaIrTe}_{4}$ : A ternary type-II Weyl semimetal
journal, May 2016

Giant and anisotropic many-body spin–orbit tunability in a strongly correlated kagome magnet
journal, September 2018

Photocurrents in Weyl semimetals
journal, January 2017

Magnetic Weyl semimetal phase in a Kagomé crystal
journal, September 2019

Fermi arc electronic structure and Chern numbers in the type-II Weyl semimetal candidate ${Mo}_{x} W_{1 - x} {Te}_{2}$
journal, August 2016

Stable Weyl points, trivial surface states, and particle-hole compensation in ${WP}_{2}$
journal, May 2018

Nodal-chain metals
journal, August 2016

Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal
journal, March 2019

Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature
journal, October 2015

Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2
journal, October 2016

Topological nodal-line fermions in spin-orbit metal PbTaSe2
journal, February 2016

Elektron und Gravitation. I
journal, May 1929

Discovery of Lorentz-violating type II Weyl fermions in LaAlGe
journal, June 2017

Topological negative refraction of surface acoustic waves in a Weyl phononic crystal
journal, August 2018

Quasiparticle interference and nonsymmorphic effect on a floating band surface state of ZrSiSe
journal, October 2018

Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal
journal, July 2018

Zero‐Field Nernst Effect in a Ferromagnetic Kagome‐Lattice Weyl‐Semimetal Co ₃ Sn ₂ S ₂
journal, April 2019

Weyl semimetals from noncentrosymmetric topological insulators
journal, October 2014

Friedel oscillations due to Fermi arcs in Weyl semimetals
journal, November 2012

Chiral magnetic effect and natural optical activity in metals with or without Weyl points
journal, December 2015

Edge conduction in monolayer WTe2
journal, April 2017

Chiral topological semimetal with multifold band crossings and long Fermi arcs
journal, May 2019

Observation of three-component fermions in the topological semimetal molybdenum phosphide
journal, June 2017

Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
journal, June 2012

Topological Materials: Quantum Anomalous Hall System
journal, March 2018

Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi
journal, February 2019

A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class
journal, June 2015

Topological semimetals
journal, October 2016

Magnetotransport properties of the type-II Weyl semimetal candidate ${Ta}_{3} S_{2}$
journal, November 2016

Three-component fermions with surface Fermi arcs in tungsten carbide
journal, January 2018

Weyl semimetals, Fermi arcs and chiral anomalies
journal, October 2016

Magnetotransport and de Haas–van Alphen measurements in the type-II Weyl semimetal ${TaIrTe}_{4}$
journal, October 2016

Dirac versus Weyl Fermions in Topological Insulators: Adler-Bell-Jackiw Anomaly in Transport Phenomena
journal, December 2013

Ultraquantum magnetoresistance in the Kramers-Weyl semimetal candidate $β {− Ag}_{2} Se$
journal, October 2017

Large, non-saturating magnetoresistance in WTe2
journal, September 2014

Topological semimetals predicted from first-principles calculations
journal, June 2016

Observation of Fermi arc surface states in a topological metal
journal, December 2014

A strongly robust type II Weyl fermion semimetal state in Ta ₃ S ₂
journal, June 2016

Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2
journal, December 2016

Topological chiral crystals with helicoid-arc quantum states
journal, March 2019

Massive Dirac fermions in a ferromagnetic kagome metal
journal, March 2018

Superconductivity in Weyl metals
journal, July 2015

Topological semimetals carrying arbitrary Hopf numbers: Fermi surface topologies of a Hopf link, Solomon's knot, trefoil knot, and other linked nodal varieties
journal, July 2017

Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2
journal, September 2016

Double-Weyl Phonons in Transition-Metal Monosilicides
journal, January 2018

Experimental discovery of a topological Weyl semimetal state in TaP
journal, November 2015

Dirac Fermions in Solids: From High-T _c Cuprates and Graphene to Topological Insulators and Weyl Semimetals
journal, March 2014

Topological Hopf and Chain Link Semimetal States and Their Application to ${Co}_{2} Mn G a$
journal, October 2017

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials
journal, November 2015

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

Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS
journal, May 2016

Topological Node-Line Semimetal and Dirac Semimetal State in Antiperovskite ${Cu}_{3} PdN$
journal, July 2015

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