Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials

Liu, F.; Qu, F.; Žutić, I.; Xie, S.; Liu, D.; Fonseca, A. A.; Malard, M.

doi:10.1021/acs.jpclett.1c01249

Title: Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials

Abstract

A nodal-line semimetal (NLSM) is suppressed in the presence of spin–orbit coupling unless it is protected by a nonsymmorphic symmetry. We show that two-dimensional (2D) materials can realize robust NLSMs when vacancies are introduced on the lattice. As a case study we investigate borophene, a boron honeycomb-like sheet. While the Dirac cones of pristine borophene are shown to be gapped out by spin–orbit coupling and by magnetic exchange, robust nodal lines (NLs) emerge in the spectrum when selected atoms are removed. We propose an effective 2D model and a symmetry analysis to demonstrate that these NLs are topological and protected by a nonsymmorphic glide plane. Finally, our findings offer a paradigm shift to the design of NLSMs: instead of searching for nonsymmorphic materials, robust NLSMs may be realized simply by removing atoms from ordinary symmorphic crystals.

Authors:

^[1]; Qu, F. ^[1]; Žutić, I. ^[2]; Xie, S. ^[3];

^[3]; Fonseca, A. A. ^[1]; Malard, M. ^[1]

Universidade de Brasília, Brasília-DF (Brazil)
State Univ. of New York (SUNY), Buffalo, NY (United States)
Shandong Univ., Jinan (China)

Publication Date:: Tue Jun 15 00:00:00 EDT 2021

Research Org.:: State Univ. of New York (SUNY), Buffalo, NY (United States)

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

OSTI Identifier:: 1831512

Grant/Contract Number:: SC0004890

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physical Chemistry Letters

Additional Journal Information:: Journal Volume: 12; Journal Issue: 24; Journal ID: ISSN 1948-7185

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats


                    Liu, F., Qu, F., Žutić, I., Xie, S., Liu, D., Fonseca, A. A., and Malard, M. Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials.  United States: N. p., 2021. 
Web.  doi:10.1021/acs.jpclett.1c01249.

Copy to clipboard


                    Liu, F., Qu, F., Žutić, I., Xie, S., Liu, D., Fonseca, A. A., & Malard, M. Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials.  United States.  https://doi.org/10.1021/acs.jpclett.1c01249

Copy to clipboard


                    Liu, F., Qu, F., Žutić, I., Xie, S., Liu, D., Fonseca, A. A., and Malard, M. Tue .  
"Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials".  United States.  https://doi.org/10.1021/acs.jpclett.1c01249.  https://www.osti.gov/servlets/purl/1831512.

Copy to clipboard


                    
@article{osti_1831512,

  title        = {Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials},

  author       = {Liu, F. and Qu, F. and Žutić, I. and Xie, S. and Liu, D. and Fonseca, A. A. and Malard, M.},

  abstractNote = {A nodal-line semimetal (NLSM) is suppressed in the presence of spin–orbit coupling unless it is protected by a nonsymmorphic symmetry. We show that two-dimensional (2D) materials can realize robust NLSMs when vacancies are introduced on the lattice. As a case study we investigate borophene, a boron honeycomb-like sheet. While the Dirac cones of pristine borophene are shown to be gapped out by spin–orbit coupling and by magnetic exchange, robust nodal lines (NLs) emerge in the spectrum when selected atoms are removed. We propose an effective 2D model and a symmetry analysis to demonstrate that these NLs are topological and protected by a nonsymmorphic glide plane. Finally, our findings offer a paradigm shift to the design of NLSMs: instead of searching for nonsymmorphic materials, robust NLSMs may be realized simply by removing atoms from ordinary symmorphic crystals.},

  doi          = {10.1021/acs.jpclett.1c01249},

  journal      = {Journal of Physical Chemistry Letters},

  number       = 24,

  volume       = 12,

  place        = {United States},

  year         = {Tue Jun 15 00:00:00 EDT 2021},

  month        = {Tue Jun 15 00:00:00 EDT 2021}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1021/acs.jpclett.1c01249

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Topological semimetals
journal, October 2016

Burkov, A. A.
Nature Materials, Vol. 15, Issue 11
DOI: 10.1038/nmat4788

Spintronics: Fundamentals and applications
journal, April 2004

Žutić, Igor; Fabian, Jaroslav; Das Sarma, S.
Reviews of Modern Physics, Vol. 76, Issue 2
DOI: 10.1103/RevModPhys.76.323

Realization of Symmetry-Enforced Two-Dimensional Dirac Fermions in Nonsymmorphic α-Bismuthene
journal, January 2020

Kowalczyk, Pawel J.; Brown, Simon A.; Maerkl, Tobias
ACS Nano, Vol. 14, Issue 2
DOI: 10.1021/acsnano.9b08136

Line-Node Dirac Semimetal and Topological Insulating Phase in Noncentrosymmetric Pnictides CaAg X ( X = P, As)
journal, January 2016

Yamakage, Ai; Yamakawa, Youichi; Tanaka, Yukio
Journal of the Physical Society of Japan, Vol. 85, Issue 1
DOI: 10.7566/JPSJ.85.013708

Evidence of topological superconductivity in planar Josephson junctions
journal, April 2019

Fornieri, Antonio; Whiticar, Alexander M.; Setiawan, F.
Nature, Vol. 569, Issue 7754
DOI: 10.1038/s41586-019-1068-8

Proximitized materials
journal, January 2019

Žutić, Igor; Matos-Abiague, Alex; Scharf, Benedikt
Materials Today, Vol. 22
DOI: 10.1016/j.mattod.2018.05.003

Majorana qubits for topological quantum computing
journal, June 2020

Aguado, Ramón; Kouwenhoven, Leo P.
Physics Today, Vol. 73, Issue 6
DOI: 10.1063/PT.3.4499

Nodal-chain metals
journal, August 2016

Bzdušek, Tomáš; Wu, QuanSheng; Rüegg, Andreas
Nature, Vol. 538, Issue 7623
DOI: 10.1038/nature19099

Experimental realization of two-dimensional boron sheets
journal, March 2016

Feng, Baojie; Zhang, Jin; Zhong, Qing
Nature Chemistry, Vol. 8, Issue 6
DOI: 10.1038/nchem.2491

$Z_{2}$ and Chiral Anomalies in Topological Dirac Semimetals
journal, September 2016

Burkov, Anton A.; Kim, Yong Baek
Physical Review Letters, Vol. 117, Issue 13
DOI: 10.1103/PhysRevLett.117.136602

An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions
journal, August 2014

Mostofi, Arash A.; Yates, Jonathan R.; Pizzi, Giovanni
Computer Physics Communications, Vol. 185, Issue 8
DOI: 10.1016/j.cpc.2014.05.003

Freestanding Borophene and Its Hybrids
journal, May 2019

Ranjan, Pranay; Sahu, Tumesh Kumar; Bhushan, Rebti
Advanced Materials, Vol. 31, Issue 27
DOI: 10.1002/adma.201900353

Unified Theory of $P T$ and $C P$ Invariant Topological Metals and Nodal Superconductors
journal, April 2016

Zhao, Y. X.; Schnyder, Andreas P.; Wang, Z. D.
Physical Review Letters, Vol. 116, Issue 15
DOI: 10.1103/PhysRevLett.116.156402

Topology of crystalline insulators and superconductors
journal, October 2014

Shiozaki, Ken; Sato, Masatoshi
Physical Review B, Vol. 90, Issue 16
DOI: 10.1103/PhysRevB.90.165114

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola
Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502
DOI: 10.1088/0953-8984/21/39/395502

Topological superconductivity in a phase-controlled Josephson junction
journal, April 2019

Ren, Hechen; Pientka, Falko; Hart, Sean
Nature, Vol. 569, Issue 7754
DOI: 10.1038/s41586-019-1148-9

Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets
journal, September 2007

Tang, Hui; Ismail-Beigi, Sohrab
Physical Review Letters, Vol. 99, Issue 11
DOI: 10.1103/PhysRevLett.99.115501

Development of a Ni-Doped VAl ₃ Topological Semimetal with a Significantly Enhanced HER Catalytic Performance
journal, April 2021

Kong, Xiang-Peng; Jiang, Tao; Gao, JiaoJiao
The Journal of Physical Chemistry Letters, Vol. 12, Issue 15
DOI: 10.1021/acs.jpclett.1c00238

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors
journal, November 2014

Chiu, Ching-Kai; Schnyder, Andreas P.
Physical Review B, Vol. 90, Issue 20
DOI: 10.1103/PhysRevB.90.205136

Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides X Te 2 ( X = Mo , W )
journal, October 2019

Wang, Zhijun; Wieder, Benjamin J.; Li, Jian
Physical Review Letters, Vol. 123, Issue 18
DOI: 10.1103/PhysRevLett.123.186401

Dirac Semimetals in Two Dimensions
journal, September 2015

Young, Steve M.; Kane, Charles L.
Physical Review Letters, Vol. 115, Issue 12
DOI: 10.1103/PhysRevLett.115.126803

Polymorphism of Two-Dimensional Boron
journal, April 2012

Penev, Evgeni S.; Bhowmick, Somnath; Sadrzadeh, Arta
Nano Letters, Vol. 12, Issue 5
DOI: 10.1021/nl3004754

Phase Signature of Topological Transition in Josephson Junctions
journal, January 2021

Dartiailh, Matthieu C.; Mayer, William; Yuan, Joseph
Physical Review Letters, Vol. 126, Issue 3
DOI: 10.1103/PhysRevLett.126.036802

Temperature Dependence of Spin–Orbit Torques in Nearly Compensated Tb ₂₁ Co ₇₉ Films by a Topological Insulator Sb ₂ Te ₃
journal, March 2021

Xue, Hongwei; Lv, Wenxing; Wu, Di
The Journal of Physical Chemistry Letters, Vol. 12, Issue 9
DOI: 10.1021/acs.jpclett.1c00378

Topological Semimetal Nanostructures: From Properties to Topotronics
journal, April 2020

Wang, An-Qi; Ye, Xing-Guo; Yu, Da-Peng
ACS Nano, Vol. 14, Issue 4
DOI: 10.1021/acsnano.9b07990

Topological response in Weyl semimetals and the chiral anomaly
journal, September 2012

Zyuzin, A. A.; Burkov, A. A.
Physical Review B, Vol. 86, Issue 11
DOI: 10.1103/PhysRevB.86.115133

Black phosphorus and its isoelectronic materials
journal, April 2019

Xia, Fengnian; Wang, Han; Hwang, James C. M.
Nature Reviews Physics, Vol. 1, Issue 5
DOI: 10.1038/s42254-019-0043-5

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice ^*
journal, May 2017

Lu, Jin-Lian; Luo, Wei; Li, Xue-Yang
Chinese Physics Letters, Vol. 34, Issue 5
DOI: 10.1088/0256-307X/34/5/057302

Crystal Growth and Magnetic Properties of Topological Nodal-Line Semimetal GdSbTe with Antiferromagnetic Spin Ordering
journal, August 2019

Sankar, Raman; Muthuselvam, I. Panneer; Babu, K. Ramesh
Inorganic Chemistry, Vol. 58, Issue 17
DOI: 10.1021/acs.inorgchem.9b01698

Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs
journal, December 2015

Mannix, A. J.; Zhou, X. -F.; Kiraly, B.
Science, Vol. 350, Issue 6267
DOI: 10.1126/science.aad1080

Effect of Confinement on the Exciton and Biexciton Dynamics in Perovskite 2D-Nanosheets and 3D-Nanocrystals
journal, July 2020

Shukla, Ayushi; Kaur, Gurpreet; Babu, K. Justice
The Journal of Physical Chemistry Letters, Vol. 11, Issue 15
DOI: 10.1021/acs.jpclett.0c01853

Borophene with Large Holes
journal, July 2020

Wang, Yong; Park, Yunjae; Qiu, Lu
The Journal of Physical Chemistry Letters, Vol. 11, Issue 15
DOI: 10.1021/acs.jpclett.0c01359

Weyl Nodal Point–Line Fermion in Ferromagnetic Eu ₅ Bi ₃
journal, April 2019

Wu, Hongbo; Ma, Da-Shuai; Fu, Botao
The Journal of Physical Chemistry Letters, Vol. 10, Issue 10
DOI: 10.1021/acs.jpclett.9b00752

d Orbital Topological Insulator and Semimetal in the Antifluorite Cu ₂ S Family: Contrasting Spin Helicities, Nodal Box, and Hybrid Surface States
journal, July 2017

Sheng, Xian-Lei; Yu, Zhi-Ming; Yu, Rui
The Journal of Physical Chemistry Letters, Vol. 8, Issue 15
DOI: 10.1021/acs.jpclett.7b01390

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

Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola
Nature Communications, Vol. 7, Issue 1
DOI: 10.1038/ncomms11696

Fabrication of Multilayer Borophene on Insulator Structure
journal, August 2016

Tsai, Hsu-Sheng; Hsiao, Ching-Hung; Lin, Yu-Pin
Small, Vol. 12, Issue 38
DOI: 10.1002/smll.201601915

Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
journal, September 2007

Shuichi Murakami,
New Journal of Physics, Vol. 9, Issue 9
DOI: 10.1088/1367-2630/9/9/356

Nonsymmorphic symmetry-required band crossings in topological semimetals
journal, November 2016

Zhao, Y. X.; Schnyder, Andreas P.
Physical Review B, Vol. 94, Issue 19
DOI: 10.1103/PhysRevB.94.195109

Origin of the Electron–Phonon Interaction of Topological Semimetal Surfaces Measured with Helium Atom Scattering
journal, February 2020

Benedek, Giorgio; Miret-Artés, Salvador; Manson, J. R.
The Journal of Physical Chemistry Letters, Vol. 11, Issue 5
DOI: 10.1021/acs.jpclett.9b03829

Extremely Large Magnetoresistance in a Topological Semimetal Candidate Pyrite ${PtBi}_{2}$
journal, June 2017

Gao, Wenshuai; Hao, Ningning; Zheng, Fa-Wei
Physical Review Letters, Vol. 118, Issue 25
DOI: 10.1103/PhysRevLett.118.256601

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

Wan, Xiangang; Turner, Ari M.; Vishwanath, Ashvin
Physical Review B, Vol. 83, Issue 20
DOI: 10.1103/PhysRevB.83.205101

Similar Records in DOE PAGES and OSTI.GOV collections:

Vacancy-engineered nodal-line semimetals

Journal Article Liu, Fujun ; Qu, Fanyao ; Žutić, Igor ; ... - Scientific Reports

Symmetry-enforced nodal-line semimetals are immune to perturbations that preserve the underlying symmetries. This intrinsic robustness enables investigations of fundamental phenomena and applications utilizing diverse materials design techniques. The drawback of symmetry-enforced nodal-line semimetals is that the crossings of energy bands are constrained to symmetry-invariant momenta in the Brillouin zone. On the other end are accidental nodal-line semimetals whose band crossings, not being enforced by symmetry, are easily destroyed by perturbations. Some accidental nodal-line semimetals have, however, the advantage that their band crossings can occur in generic locations in the Brillouin zone, and thus can be repositioned to tailor material properties.more »« less
https://doi.org/10.1038/s41598-022-18519-8

Full Text Available
Topological nodal line semimetals with and without spin-orbital coupling

Journal Article Fang, Chen ; Chen, Yige ; Kee, Hae -Young ; ... - Physical Review. B, Condensed Matter and Materials Physics

Here, we theoretically study three-dimensional topological semimetals (TSMs) with nodal lines protected by crystalline symmetries. Compared to TSMs with point nodes, e.g., Weyl semimetals and Dirac semimetals, where the conduction and the valence bands touch at discrete points, in these TSMs the two bands cross at closed lines in the Brillouin zone. We propose two different classes of symmetry protected nodal lines in the absence and in the presence of spin-orbital coupling (SOC), respectively. In the former, we discuss nodal lines that are protected by a combination of inversion symmetry and time-reversal symmetry, yet, unlike previously studied nodal lines inmore »« less
Cited by 631
https://doi.org/10.1103/physrevb.92.081201

Full Text Available
A 2D nonsymmorphic Dirac semimetal in a chemically modified group-VA monolayer with a black phosphorene structure

Journal Article Jin, Kyung-Hwan ; Huang, Huaqing ; Wang, Zhengfei ; ... - Nanoscale

A symmetry-protected 2D Dirac semimetal has attracted intense interest for its intriguing material properties. In this paper, we report a 2D nonsymmorphic Dirac semimetal state in a chemically modified group-VA 2D puckered structure. Based on first-principles calculations, we demonstrate the existence of 2D Dirac fermions in a one-side modified phosphorene structure in two different types: one with a Dirac nodal line (DNL) structure for light elements with negligible spin–orbit coupling (SOC) and the other having an hourglass band protected by a nonsymmorphic symmetry for heavy elements with strong SOC. In the absence of SOC, the DNL exhibits an anisotropic behaviormore »« less
Cited by 20
https://doi.org/10.1039/c9nr00906j

Full Text Available
Observation of nodal line in non-symmorphic topological semimetal InBi

Journal Article Ekahana, Sandy Adhitia ; Wu, Shu-Chun ; Jiang, Juan ; ... - New Journal of Physics

Topological nodal semimetal (TNS), characterized by its touching conduction and valence bands, is a newly discovered state of quantum matter which exhibits various exotic physical phenomena. Recently, a new type of TNS called topological nodal line semimetal (TNLS) is predicted where its conduction and valence band form a degenerate one-dimension line which is further protected by its crystal symmetry. In this work, we systematically investigated the bulk and surface electronic structure of the non-symmorphic, TNLS in InBi (which is also a type II Dirac semimetal) with strong spin–orbit coupling by using angle resolved photoemission spectroscopy. By tracking the crossing points of the bulk bands at the Brillouin zone boundary, we discovered the nodal-line feature along themore »« less
Cited by 46
https://doi.org/10.1088/1367-2630/aa75a1

Full Text Available
Realization of a Type-II Nodal-Line Semimetal in Mg₃Bi₂

Journal Article Chang, Tay-Rong ; Pletikosic, Ivo ; Kong, Tai ; ... - Advanced Science

Nodal-line semimetals (NLSs) represent a new type of topological semimetallic phase beyond Weyl and Dirac semimetals in the sense that they host closed loops or open curves of band degeneracies in the Brillouin zone. Parallel to the classification of type-I and type-II Weyl semimetals, there are two types of NLSs. The type-I NLS phase has been proposed and realized in many compounds, whereas the exotic type-II NLS phase that strongly violates Lorentz symmetry has remained elusive. First-principles calculations show that Mg₃Bi₂ is a material candidate for the type-II NLS. The band crossing is close to the Fermi level and exhibitsmore »« less
Cited by 64
https://doi.org/10.1002/advs.201800897

Full Text Available

Similar Records

Title: Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials

Abstract

Citation Formats

Topological semimetals journal, October 2016

Spintronics: Fundamentals and applications journal, April 2004

Realization of Symmetry-Enforced Two-Dimensional Dirac Fermions in Nonsymmorphic α-Bismuthene journal, January 2020

Line-Node Dirac Semimetal and Topological Insulating Phase in Noncentrosymmetric Pnictides CaAg X ( X = P, As) journal, January 2016

Evidence of topological superconductivity in planar Josephson junctions journal, April 2019

Proximitized materials journal, January 2019

Majorana qubits for topological quantum computing journal, June 2020

Nodal-chain metals journal, August 2016

Experimental realization of two-dimensional boron sheets journal, March 2016

Z 2 and Chiral Anomalies in Topological Dirac Semimetals journal, September 2016

An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions journal, August 2014

Freestanding Borophene and Its Hybrids journal, May 2019

Unified Theory of P T and C P Invariant Topological Metals and Nodal Superconductors journal, April 2016

Topology of crystalline insulators and superconductors journal, October 2014

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials journal, September 2009

Topological superconductivity in a phase-controlled Josephson junction journal, April 2019

Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets journal, September 2007

Development of a Ni-Doped VAl 3 Topological Semimetal with a Significantly Enhanced HER Catalytic Performance journal, April 2021

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors journal, November 2014

Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides X Te 2 ( X = Mo , W ) journal, October 2019

Dirac Semimetals in Two Dimensions journal, September 2015

Polymorphism of Two-Dimensional Boron journal, April 2012

Phase Signature of Topological Transition in Josephson Junctions journal, January 2021

Temperature Dependence of Spin–Orbit Torques in Nearly Compensated Tb 21 Co 79 Films by a Topological Insulator Sb 2 Te 3 journal, March 2021

Topological Semimetal Nanostructures: From Properties to Topotronics journal, April 2020

Topological response in Weyl semimetals and the chiral anomaly journal, September 2012

Black phosphorus and its isoelectronic materials journal, April 2019

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice * journal, May 2017

Crystal Growth and Magnetic Properties of Topological Nodal-Line Semimetal GdSbTe with Antiferromagnetic Spin Ordering journal, August 2019

Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs journal, December 2015

Effect of Confinement on the Exciton and Biexciton Dynamics in Perovskite 2D-Nanosheets and 3D-Nanocrystals journal, July 2020

Borophene with Large Holes journal, July 2020

Weyl Nodal Point–Line Fermion in Ferromagnetic Eu 5 Bi 3 journal, April 2019

d Orbital Topological Insulator and Semimetal in the Antifluorite Cu 2 S Family: Contrasting Spin Helicities, Nodal Box, and Hybrid Surface States journal, July 2017

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

Fabrication of Multilayer Borophene on Insulator Structure journal, August 2016

Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase journal, September 2007

Nonsymmorphic symmetry-required band crossings in topological semimetals journal, November 2016

Origin of the Electron–Phonon Interaction of Topological Semimetal Surfaces Measured with Helium Atom Scattering journal, February 2020

Extremely Large Magnetoresistance in a Topological Semimetal Candidate Pyrite PtBi 2 journal, June 2017

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

Topological semimetals
journal, October 2016

Spintronics: Fundamentals and applications
journal, April 2004

Realization of Symmetry-Enforced Two-Dimensional Dirac Fermions in Nonsymmorphic α-Bismuthene
journal, January 2020

Line-Node Dirac Semimetal and Topological Insulating Phase in Noncentrosymmetric Pnictides CaAg X ( X = P, As)
journal, January 2016

Evidence of topological superconductivity in planar Josephson junctions
journal, April 2019

Proximitized materials
journal, January 2019

Majorana qubits for topological quantum computing
journal, June 2020

Nodal-chain metals
journal, August 2016

Experimental realization of two-dimensional boron sheets
journal, March 2016

$Z_{2}$ and Chiral Anomalies in Topological Dirac Semimetals
journal, September 2016

An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions
journal, August 2014

Freestanding Borophene and Its Hybrids
journal, May 2019

Unified Theory of $P T$ and $C P$ Invariant Topological Metals and Nodal Superconductors
journal, April 2016

Topology of crystalline insulators and superconductors
journal, October 2014

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

Topological superconductivity in a phase-controlled Josephson junction
journal, April 2019

Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets
journal, September 2007

Development of a Ni-Doped VAl ₃ Topological Semimetal with a Significantly Enhanced HER Catalytic Performance
journal, April 2021

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors
journal, November 2014

Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides X Te 2 ( X = Mo , W )
journal, October 2019

Dirac Semimetals in Two Dimensions
journal, September 2015

Polymorphism of Two-Dimensional Boron
journal, April 2012

Phase Signature of Topological Transition in Josephson Junctions
journal, January 2021

Temperature Dependence of Spin–Orbit Torques in Nearly Compensated Tb ₂₁ Co ₇₉ Films by a Topological Insulator Sb ₂ Te ₃
journal, March 2021

Topological Semimetal Nanostructures: From Properties to Topotronics
journal, April 2020

Topological response in Weyl semimetals and the chiral anomaly
journal, September 2012

Black phosphorus and its isoelectronic materials
journal, April 2019

Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice ^*
journal, May 2017

Crystal Growth and Magnetic Properties of Topological Nodal-Line Semimetal GdSbTe with Antiferromagnetic Spin Ordering
journal, August 2019

Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs
journal, December 2015

Effect of Confinement on the Exciton and Biexciton Dynamics in Perovskite 2D-Nanosheets and 3D-Nanocrystals
journal, July 2020

Borophene with Large Holes
journal, July 2020

Weyl Nodal Point–Line Fermion in Ferromagnetic Eu ₅ Bi ₃
journal, April 2019

d Orbital Topological Insulator and Semimetal in the Antifluorite Cu ₂ S Family: Contrasting Spin Helicities, Nodal Box, and Hybrid Surface States
journal, July 2017

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

Fabrication of Multilayer Borophene on Insulator Structure
journal, August 2016

Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
journal, September 2007

Nonsymmorphic symmetry-required band crossings in topological semimetals
journal, November 2016

Origin of the Electron–Phonon Interaction of Topological Semimetal Surfaces Measured with Helium Atom Scattering
journal, February 2020

Extremely Large Magnetoresistance in a Topological Semimetal Candidate Pyrite ${PtBi}_{2}$
journal, June 2017

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