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Title: Building blocks of topological quantum chemistry: Elementary band representations


Not provided.

; ; ; ; ; ; ;
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
DOE Contract Number:  
Resource Type:
Journal Article
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 97; Journal Issue: 3; Journal ID: ISSN 2469-9950
American Physical Society (APS)
Country of Publication:
United States
Materials Science; Physics

Citation Formats

Cano, Jennifer, Bradlyn, Barry, Wang, Zhijun, Elcoro, L., Vergniory, M. G., Felser, C., Aroyo, M. I., and Bernevig, B. Andrei. Building blocks of topological quantum chemistry: Elementary band representations. United States: N. p., 2018. Web. doi:10.1103/physrevb.97.035139.
Cano, Jennifer, Bradlyn, Barry, Wang, Zhijun, Elcoro, L., Vergniory, M. G., Felser, C., Aroyo, M. I., & Bernevig, B. Andrei. Building blocks of topological quantum chemistry: Elementary band representations. United States. doi:10.1103/physrevb.97.035139.
Cano, Jennifer, Bradlyn, Barry, Wang, Zhijun, Elcoro, L., Vergniory, M. G., Felser, C., Aroyo, M. I., and Bernevig, B. Andrei. Mon . "Building blocks of topological quantum chemistry: Elementary band representations". United States. doi:10.1103/physrevb.97.035139.
title = {Building blocks of topological quantum chemistry: Elementary band representations},
author = {Cano, Jennifer and Bradlyn, Barry and Wang, Zhijun and Elcoro, L. and Vergniory, M. G. and Felser, C. and Aroyo, M. I. and Bernevig, B. Andrei},
abstractNote = {Not provided.},
doi = {10.1103/physrevb.97.035139},
journal = {Physical Review B},
issn = {2469-9950},
number = 3,
volume = 97,
place = {United States},
year = {2018},
month = {1}

Works referenced in this record:

Symmetry Specification of Bands in Solids
journal, September 1980

Band representations and symmetry types of bands in solids
journal, March 1981

Connectivity of energy bands in crystals
journal, March 1999

Elementary energy bands in crystalline solids
journal, May 2000

Elementary energy bands in crystals are connected
journal, February 2001

Topological quantum chemistry
journal, July 2017

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

Topological order and absence of band insulators at integer filling in non-symmorphic crystals
journal, April 2013

  • Parameswaran, Siddharth A.; Turner, Ari M.; Arovas, Daniel P.
  • Nature Physics, Vol. 9, Issue 5
  • DOI: 10.1038/nphys2600

Filling-enforced quantum band insulators in spin-orbit coupled crystals
journal, April 2016

  • Po, Hoi Chun; Watanabe, Haruki; Zaletel, Michael P.
  • Science Advances, Vol. 2, Issue 4
  • DOI: 10.1126/sciadv.1501782

Double crystallographic groups and their representations on the Bilbao Crystallographic Server
journal, September 2017

  • Elcoro, Luis; Bradlyn, Barry; Wang, Zhijun
  • Journal of Applied Crystallography, Vol. 50, Issue 5
  • DOI: 10.1107/S1600576717011712

Band connectivity for topological quantum chemistry: Band structures as a graph theory problem
journal, January 2018

Graph theory data for topological quantum chemistry
journal, August 2017

Symmetry and Analyticity of Energy Bands in Solids
journal, August 1988

Duals of crystallographic groups. Band and quasi-band representations
journal, April 1993

  • Bacry, Henri
  • Communications in Mathematical Physics, Vol. 153, Issue 2
  • DOI: 10.1007/BF02096648

Physical Equivalence of Energy Bands in Solids
journal, February 1992

Equivalent expression of Z 2 topological invariant for band insulators using the non-Abelian Berry connection
journal, August 2011

Wannier representation of Z 2 topological insulators
journal, January 2011

Berry-phase description of topological crystalline insulators
journal, May 2016

Topological Insulators from Group Cohomology
journal, April 2016

Quantized electric multipole insulators
journal, July 2017

  • Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L.
  • Science, Vol. 357, Issue 6346
  • DOI: 10.1126/science.aah6442

Topological insulators with inversion symmetry
journal, July 2007

Surface states and topological invariants in three-dimensional topological insulators: Application to Bi1xSbx
journal, July 2008

  • Teo, Jeffrey C. Y.; Fu, Liang; Kane, C. L.
  • Physical Review B, Vol. 78, Issue 4, Article No. 045426
  • DOI: 10.1103/PhysRevB.78.045426

Inversion-symmetric topological insulators
journal, June 2011

Bulk topological invariants in noninteracting point group symmetric insulators
journal, September 2012

Entanglement and inversion symmetry in topological insulators
journal, December 2010

Topological Crystalline Insulators
journal, March 2011

Quantized response and topology of magnetic insulators with inversion symmetry
journal, April 2012

Topological classification with additional symmetries from Clifford algebras
journal, September 2013

Classification of topological insulators and superconductors in the presence of reflection symmetry
journal, August 2013

Topological classification of crystalline insulators with space group symmetry
journal, August 2013

Topological nonsymmorphic crystalline insulators
journal, August 2014

Topology of crystalline insulators and superconductors
journal, October 2014

Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry
journal, September 2014

New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic
journal, April 2015

Z 2 topology in nonsymmorphic crystalline insulators: Möbius twist in surface states
journal, April 2015

Topological magnetic crystalline insulators and corepresentation theory
journal, March 2015

Classification of topological quantum matter with symmetries
journal, August 2016

Classification of topological crystalline insulators based on representation theory
journal, January 2016

Symmetry-protected topological photonic crystal in three dimensions
journal, January 2016

  • Lu, Ling; Fang, Chen; Fu, Liang
  • Nature Physics, Vol. 12, Issue 4
  • DOI: 10.1038/nphys3611

Dirac Semimetal in Three Dimensions
journal, April 2012

Protected boundary states in gapless topological phases
journal, June 2013

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

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

Bulk Dirac Points in Distorted Spinels
journal, January 2014

Classification of crystalline topological semimetals with an application to Na 3 Bi
journal, April 2015

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

Topological charges of three-dimensional Dirac semimetals with rotation symmetry
journal, October 2015

Dirac Semimetals in Two Dimensions
journal, September 2015

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

Ca 3 P 2 and other topological semimetals with line nodes and drumhead surface states
journal, May 2016

Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
journal, August 2016

Spin-orbit semimetals in the layer groups
journal, October 2016

Double Dirac Semimetals in Three Dimensions
journal, May 2016

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

The space group classification of topological band-insulators
journal, December 2012

  • Slager, Robert-Jan; Mesaros, Andrej; Juričić, Vladimir
  • Nature Physics, Vol. 9, Issue 2
  • DOI: 10.1038/nphys2513

Topological Classification of Crystalline Insulators through Band Structure Combinatorics
journal, December 2017

Symmetry-based indicators of band topology in the 230 space groups
journal, June 2017

Twisted Equivariant Matter
journal, March 2013

Compactly supported Wannier functions and algebraic K -theory
journal, March 2017

Topological crystalline materials: General formulation, module structure, and wallpaper groups
journal, June 2017

Comments on the decomposition of the regular representation of crystallographic space groups into band representations
journal, February 2000

  • Zeiner, P.; Dirl, R.; Davies, B. L.
  • Journal of Physics A: Mathematical and General, Vol. 33, Issue 8
  • DOI: 10.1088/0305-4470/33/8/308

Smooth gauge for topological insulators
journal, March 2012

Analytic Properties of Bloch Waves and Wannier Functions
journal, August 1959

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups
journal, March 2006

  • Aroyo, Mois I.; Kirov, Asen; Capillas, Cesar
  • Acta Crystallographica Section A Foundations of Crystallography, Vol. 62, Issue 2
  • DOI: 10.1107/S0108767305040286

Bilbao Crystallographic Server: I. Databases and crystallographic computing programs
journal, January 2006

  • Aroyo, Mois Ilia; Perez-Mato, Juan Manuel; Capillas, Cesar
  • Zeitschrift für Kristallographie - Crystalline Materials, Vol. 221, Issue 1
  • DOI: 10.1524/zkri.2006.221.1.15

Accidental Degeneracy in the Energy Bands of Crystals
journal, August 1937

Solitons in Polyacetylene
journal, June 1979

Elementary Excitations of a Linearly Conjugated Diatomic Polymer
journal, November 1982

Quantum Spin Hall Effect in Graphene
journal, November 2005

Berry’s phase for energy bands in solids
journal, June 1989

Theory of polarization of crystalline solids
journal, January 1993