Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5

Chen, Zhi -Guo; Chen, R. Y.; Zhong, R. D.; Schneeloch, John; Zhang, C.; Huang, Y.; Qu, Fanming; Yu, Rui; Li, Q.; Gu, G. D.; Wang, N. L.

doi:10.1073/pnas.1613110114

Title: Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe₅

Abstract

Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by time-reversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe₅, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [~33,000 cm²/(V • s)] multilayer ZrTe₅ flake at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ~10 meV and a √B dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Finally, our results not only provide spectroscopic evidence for the TI statemore »« less

Authors:

Chen, Zhi -Guo ^[1]; Chen, R. Y. ^[2]; Zhong, R. D. ^[3]; Schneeloch, John ^[3]; Zhang, C. ^[3]; Huang, Y. ^[3]; Qu, Fanming ^[4]; Yu, Rui ^[5];

^[3]; Gu, G. D. ^[3]; Wang, N. L. ^[6]

Chinese Academy of Sciences (CAS), Beijing (China)
Peking Univ., Beijing (China)
Brookhaven National Lab. (BNL), Upton, NY (United States)
Chinese Academy of Sciences (CAS), Beijing (China); Delft Univ. of Technology, Delft (The Netherlands)
Wuhan Univ., Wuhan (China)
Peking Univ., Beijing (China); Collaborative Innovation Center of Quantum Matter, Beijing (China)

Publication Date:: 2017-01-17

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

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

OSTI Identifier:: 1354629

Report Number(s):: BNL-113757-2017-JA
Journal ID: ISSN 0027-8424; R&D Project: PO010; KC0201060

Grant/Contract Number:: SC00112704

Resource Type:: Accepted Manuscript

Journal Name:: Proceedings of the National Academy of Sciences of the United States of America

Additional Journal Information:: Journal Volume: 114; Journal Issue: 5; Journal ID: ISSN 0027-8424

Publisher:: National Academy of Sciences, Washington, DC (United States)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; band inversion; Dirac fermions; topological insulators; Landau levels; Zeeman splitting

Citation Formats


                    Chen, Zhi -Guo, Chen, R. Y., Zhong, R. D., Schneeloch, John, Zhang, C., Huang, Y., Qu, Fanming, Yu, Rui, Li, Q., Gu, G. D., and Wang, N. L. Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5.  United States: N. p., 2017. 
Web.  doi:10.1073/pnas.1613110114.

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                    Chen, Zhi -Guo, Chen, R. Y., Zhong, R. D., Schneeloch, John, Zhang, C., Huang, Y., Qu, Fanming, Yu, Rui, Li, Q., Gu, G. D., & Wang, N. L. Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5.  United States.  https://doi.org/10.1073/pnas.1613110114

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                    Chen, Zhi -Guo, Chen, R. Y., Zhong, R. D., Schneeloch, John, Zhang, C., Huang, Y., Qu, Fanming, Yu, Rui, Li, Q., Gu, G. D., and Wang, N. L. Tue .  
"Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5".  United States.  https://doi.org/10.1073/pnas.1613110114.  https://www.osti.gov/servlets/purl/1354629.

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@article{osti_1354629,

  title        = {Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5},

  author       = {Chen, Zhi -Guo and Chen, R. Y. and Zhong, R. D. and Schneeloch, John and Zhang, C. and Huang, Y. and Qu, Fanming and Yu, Rui and Li, Q. and Gu, G. D. and Wang, N. L.},

  abstractNote = {Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by time-reversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe5, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [~33,000 cm2/(V • s)] multilayer ZrTe5 flake at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ~10 meV and a √B dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Finally, our results not only provide spectroscopic evidence for the TI state in ZrTe5 but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials.},

  doi          = {10.1073/pnas.1613110114},

  journal      = {Proceedings of the National Academy of Sciences of the United States of America},

  number       = 5,

  volume       = 114,

  place        = {United States},

  year         = {2017},

  month        = {1}

}

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Zirconium pentatelluride ZrTe₅ is a topological semimetal. The presence of a temperature-induced Lifshitz transition, in which the Fermi level goes from the conduction band to the valence band with increasing temperature, provides unique opportunities to study the interplay between Fermi-surface topology, dynamics of Dirac fermions, and Berry curvature in one system. Here we present a combined experimental and theoretical study and show that a low-energy model can be used to understand the complicated Hall response and large anomalous Hall effect observed in ZrTe₅ over a wide range of temperature and magnetic field. We found that the anomalous Hall contribution dominatesmore »« less
https://doi.org/10.1103/physrevb.106.l081124
Three-dimensional nature of the band structure of ${ZrTe}_{5}$ measured by high-momentum-resolution photoemission spectroscopy [3D nature ${ZrTe}_{5}$ band structure measured by high-momentum-resolution photoemission spectroscopy]

Journal Article Xiong, H. ; Sobota, J. A. ; Yang, S. -L. ; ... - Physical Review B

Here, we have performed a systematic high-momentum-resolution photoemission study on ZrTe₅ using 6-eV photon energy. We have measured the band structure near the Γ point, and quantified the gap between the conduction and valence band as 18 ≤ Δ ≤ 29 meV. We have also observed photon-energy-dependent behavior attributed to final-state effects and the three-dimensional (3D) nature of the material's band structure. Our interpretation indicates the gap is intrinsic and reconciles discrepancies on the existence of a topological surface state reported by different studies. The existence of a gap suggests that ZrTe₅ is not a 3D strong topological insulator normore »« less
Cited by 7
https://doi.org/10.1103/PhysRevB.95.195119

Full Text Available
Evidence for a strain-tuned topological phase transition in ZrTe₅

Journal Article Mutch, Joshua ; Chen, Wei-Chih ; Went, Preston ; ... - Science Advances

A phase transition between topologically distinct insulating phases involves closing and reopening the bandgap. Near the topological phase transition, the bulk energy spectrum is characterized by a massive Dirac dispersion, where the bandgap plays the role of mass. We report measurements of strain dependence of electrical transport properties of ZrTe₅, which is known to host massive Dirac fermions in the bulk due to its proximity to a topological phase transition. We observe that the resistivity exhibits a pronounced minimum at a critical strain. We further find that the positive longitudinal magnetoconductance becomes maximal at the critical strain. This nonmonotonic strainmore »« less
Cited by 9
https://doi.org/10.1126/sciadv.aav9771

Full Text Available
Local corrugation and persistent charge density wave in $ZrTe_{3}$ with Ni intercalation

Journal Article Ganose, Alex M. ; Gannon, Liam ; Fabrizi, Federica ; ... - Physical Review B

Here, the mechanism of emergent bulk superconductivity in transition-metal intercalated ZrTe₃ is investigated by studying the effect of Ni doping on the band structure and charge density wave (CDW). The study reports theoretical and experimental results in the range of Ni_0.01ZrTe₃ to Ni_0.05ZrTe₃. In the highest doped samples, bulk superconductivity with T_c < T_CDW is observed, with a reduced T_CDW compared with pure ZrTe₃. Relativistic ab initio calculations reveal that Ni incorporation occurs preferentially through intercalation in the van der Waals gap. Analysis of the structural and electronic effects of intercalation indicate buckling of the Te sheets adjacent to themore »« less
Cited by 3
https://doi.org/10.1103/PhysRevB.97.155103

Full Text Available

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Title: Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5

Abstract

Citation Formats

Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs text, January 2015

Landau Level Spectroscopy of Ultrathin Graphite Layers journal, December 2006

Dirac charge dynamics in graphene by infrared spectroscopy journal, June 2008

Infrared spectroscopy of Landau levels in graphene text, January 2007

Three-dimensional Dirac semimetal and quantum transport in Cd 3 As 2 journal, September 2013

Quantum Spin Hall Insulator State in HgTe Quantum Wells journal, November 2007

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

Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3 journal, June 2009

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells journal, December 2006

Weyl Semimetal in a Topological Insulator Multilayer text, January 2011

Dirac Semimetal in Three Dimensions journal, April 2012

Observation of an intrinsic bandgap and Landau level renormalization in graphene/boron-nitride heterostructures text, January 2014

A topological Dirac insulator in a quantum spin Hall phase journal, April 2008

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells text, January 2006

Experimental Realization of a Three-Dimensional Dirac Semimetal text, January 2013

Optical spectroscopy study of the three-dimensional Dirac semimetal ZrTe 5 journal, August 2015

Topological Insulators in Three Dimensions text, January 2006

Magnetoinfrared Spectroscopy of Landau Levels and Zeeman Splitting of Three-Dimensional Massless Dirac Fermions in ZrTe 5 journal, October 2015

Observation of Weyl nodes in TaAs journal, August 2015

Observation of three-dimensional massless Kane fermions in a zinc-blende crystal journal, January 2014

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

Observation of Weyl nodes in TaAs text, January 2015

Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2 journal, November 2014

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2 journal, June 2014

Infrared Spectroscopy of Landau Levels of Graphene journal, May 2007

Model Hamiltonian for topological insulators journal, July 2010

Transport evidence for the three-dimensional Dirac semimetal phase in ZrT e 5 journal, March 2016

Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices journal, May 2013

Z2 Topological Order and the Quantum Spin Hall Effect journal, September 2005

Cloning of Dirac fermions in graphene superlattices journal, May 2013

Magneto-Optics of Massive Dirac Fermions in Bulk Bi 2 Se 3 journal, May 2015

Evidence for massive bulk Dirac fermions in Pb1−xSnxSe from Nernst and thermopower experiments journal, November 2013

Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2 journal, May 2014

Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi journal, January 2014

Weyl Semimetal in a Topological Insulator Multilayer journal, September 2011

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface journal, May 2009

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

Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP journal, June 2015

Structural properties of ZrTe5 and HfTe5 as seen by powder diffraction journal, October 1986

Topological Insulators in Three Dimensions journal, March 2007

Dirac semimetal and topological phase transitions in A 3 Bi ( A = Na , K, Rb) journal, May 2012

Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi text, January 2013

Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure journal, May 2013

Fermi surface, effective masses, and Dingle temperatures of ZrTe 5 as derived from the Shubnikov – de Haas effect journal, June 1985

Topological invariants of time-reversal-invariant band structures text, January 2006

Experimental Observation of Topological Edge States at the Surface Step Edge of the Topological Insulator ZrTe 5 journal, April 2016

Experimental Realization of a Three-Dimensional Dirac Semimetal journal, July 2014

Quantum Transport Evidence for the Three-Dimensional Dirac Semimetal Phase in Cd 3 As 2 journal, December 2014

Landau level spectroscopy of ultrathin graphite layers text, January 2006

Topological invariants of time-reversal-invariant band structures journal, March 2007

Chiral magnetic effect in ZrTe5 journal, February 2016

Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd$_3$As$_2$ text, January 2014

Observation of quasi-two-dimensional Dirac fermions in ZrTe5 journal, November 2016

Cloning of Dirac fermions in graphene superlattices text, January 2012

A stable three-dimensional topological Dirac semimetal Cd3As2 journal, May 2014

Observation of an intrinsic bandgap and Landau level renormalization in graphene/boron-nitride heterostructures journal, July 2014

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

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

Electronic evidence of temperature-induced Lifshitz transition and topological nature in ZrTe5 journal, May 2017

Unraveling the topology of ZrTe 5 by changing temperature journal, December 2019

Magnetization-Induced Band Shift in Ferromagnetic Weyl Semimetal Co 3 Sn 2 S 2 journal, February 2020

Evidence for a strain-tuned topological phase transition in ZrTe 5 journal, August 2019

Magneto-optical probe of the fully gapped Dirac band in ZrSiS journal, November 2019

Thickness-Dependent In-Plane Thermal Conductivity and Enhanced Thermoelectric Performance in p-Type ZrTe 5 Nanoribbons journal, November 2018

Experimental progress on layered topological semimetals journal, April 2019

Optical signatures of Dirac nodal lines in NbAs 2 journal, December 2018

Evidence for a strain tuned topological phase transition in ZrTe5 text, January 2018

Thermoelectric transport coefficients of a Dirac electron gas in high magnetic fields journal, October 2019

Thickness-tuned transition of band topology in ZrT e 5 nanosheets journal, March 2017

Vanishing quantum oscillations in Dirac semimetal ZrTe 5 journal, August 2018

Optical spectroscopy study of the topological property in PrSb journal, September 2019

Two-Dimensional Conical Dispersion in ZrTe 5 Evidenced by Optical Spectroscopy journal, May 2019

Ultrafast hot carrier dynamics of ZrTe 5 from time-resolved optical reflectivity journal, March 2019

Magneto-optical probe of the fully gapped Dirac band in ZrSiS text, January 2019

Magnetoresistance of a three-dimensional Dirac gas journal, November 2018

Experimental Progress on Layered Topological Semimetals text, January 2019

Negative Longitudinal Magnetoresistance from the Anomalous N = 0 Landau Level in Topological Materials journal, September 2017

Title: Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe₅

Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
text, January 2015

Landau Level Spectroscopy of Ultrathin Graphite Layers
journal, December 2006

Dirac charge dynamics in graphene by infrared spectroscopy
journal, June 2008

Infrared spectroscopy of Landau levels in graphene
text, January 2007

Three-dimensional Dirac semimetal and quantum transport in Cd $_{3}$ As $_{2}$
journal, September 2013

Quantum Spin Hall Insulator State in HgTe Quantum Wells
journal, November 2007

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

Experimental Realization of a Three-Dimensional Topological Insulator, Bi₂Te₃
journal, June 2009

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
journal, December 2006

Weyl Semimetal in a Topological Insulator Multilayer
text, January 2011

Dirac Semimetal in Three Dimensions
journal, April 2012

Observation of an intrinsic bandgap and Landau level renormalization in graphene/boron-nitride heterostructures
text, January 2014

A topological Dirac insulator in a quantum spin Hall phase
journal, April 2008

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
text, January 2006

Experimental Realization of a Three-Dimensional Dirac Semimetal
text, January 2013

Optical spectroscopy study of the three-dimensional Dirac semimetal ${ZrTe}_{5}$
journal, August 2015

Topological Insulators in Three Dimensions
text, January 2006

Magnetoinfrared Spectroscopy of Landau Levels and Zeeman Splitting of Three-Dimensional Massless Dirac Fermions in ${ZrTe}_{5}$
journal, October 2015

Observation of Weyl nodes in TaAs
journal, August 2015

Observation of three-dimensional massless Kane fermions in a zinc-blende crystal
journal, January 2014

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

Observation of Weyl nodes in TaAs
text, January 2015

Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2
journal, November 2014

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2
journal, June 2014

Infrared Spectroscopy of Landau Levels of Graphene
journal, May 2007

Model Hamiltonian for topological insulators
journal, July 2010

Transport evidence for the three-dimensional Dirac semimetal phase in $ZrT e_{5}$
journal, March 2016

Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices
journal, May 2013

$Z_{2}$ Topological Order and the Quantum Spin Hall Effect
journal, September 2005

Cloning of Dirac fermions in graphene superlattices
journal, May 2013

Magneto-Optics of Massive Dirac Fermions in Bulk ${Bi}_{2} {Se}_{3}$
journal, May 2015

Evidence for massive bulk Dirac fermions in Pb1−xSnxSe from Nernst and thermopower experiments
journal, November 2013

Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2
journal, May 2014

Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi
journal, January 2014

Weyl Semimetal in a Topological Insulator Multilayer
journal, September 2011

Topological insulators in Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ with a single Dirac cone on the surface
journal, May 2009

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

Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP
journal, June 2015

Structural properties of ZrTe5 and HfTe5 as seen by powder diffraction
journal, October 1986

Topological Insulators in Three Dimensions
journal, March 2007

Dirac semimetal and topological phase transitions in $A_{3}$ Bi ( $A = Na$ , K, Rb)
journal, May 2012

Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
text, January 2013

Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure
journal, May 2013

Fermi surface, effective masses, and Dingle temperatures of ${ZrTe}_{5}$ as derived from the Shubnikov – de Haas effect
journal, June 1985

Topological invariants of time-reversal-invariant band structures
text, January 2006

Experimental Observation of Topological Edge States at the Surface Step Edge of the Topological Insulator ${ZrTe}_{5}$
journal, April 2016

Experimental Realization of a Three-Dimensional Dirac Semimetal
journal, July 2014

Quantum Transport Evidence for the Three-Dimensional Dirac Semimetal Phase in ${Cd}_{3} {As}_{2}$
journal, December 2014

Landau level spectroscopy of ultrathin graphite layers
text, January 2006

Topological invariants of time-reversal-invariant band structures
journal, March 2007

Chiral magnetic effect in ZrTe5
journal, February 2016

Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd$_3$As$_2$
text, January 2014

Observation of quasi-two-dimensional Dirac fermions in ZrTe5
journal, November 2016

Cloning of Dirac fermions in graphene superlattices
text, January 2012

A stable three-dimensional topological Dirac semimetal Cd3As2
journal, May 2014

Observation of an intrinsic bandgap and Landau level renormalization in graphene/boron-nitride heterostructures
journal, July 2014

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

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

Electronic evidence of temperature-induced Lifshitz transition and topological nature in ZrTe5
journal, May 2017

Unraveling the topology of ${ZrTe}_{5}$ by changing temperature
journal, December 2019

Magnetization-Induced Band Shift in Ferromagnetic Weyl Semimetal ${Co}_{3} {Sn}_{2} S_{2}$
journal, February 2020

Evidence for a strain-tuned topological phase transition in ZrTe ₅
journal, August 2019

Magneto-optical probe of the fully gapped Dirac band in ZrSiS
journal, November 2019

Thickness-Dependent In-Plane Thermal Conductivity and Enhanced Thermoelectric Performance in p-Type ZrTe ₅ Nanoribbons
journal, November 2018

Experimental progress on layered topological semimetals
journal, April 2019

Optical signatures of Dirac nodal lines in NbAs ₂
journal, December 2018

Evidence for a strain tuned topological phase transition in ZrTe5
text, January 2018

Thermoelectric transport coefficients of a Dirac electron gas in high magnetic fields
journal, October 2019

Thickness-tuned transition of band topology in $ZrT e_{5}$ nanosheets
journal, March 2017

Vanishing quantum oscillations in Dirac semimetal ZrTe ₅
journal, August 2018

Optical spectroscopy study of the topological property in PrSb
journal, September 2019

Two-Dimensional Conical Dispersion in ${ZrTe}_{5}$ Evidenced by Optical Spectroscopy
journal, May 2019

Ultrafast hot carrier dynamics of ${ZrTe}_{5}$ from time-resolved optical reflectivity
journal, March 2019

Magneto-optical probe of the fully gapped Dirac band in ZrSiS
text, January 2019

Magnetoresistance of a three-dimensional Dirac gas
journal, November 2018

Experimental Progress on Layered Topological Semimetals
text, January 2019

Negative Longitudinal Magnetoresistance from the Anomalous N = 0 Landau Level in Topological Materials
journal, September 2017

Thermoelectric transport coefficients of a Dirac electron gas in high magnetic fields
text, January 2019

Detection of sub-MeV dark matter with three-dimensional Dirac materials
journal, January 2018