IrRep: Symmetry eigenvalues and irreducible representations of ab initio band structures
Abstract
Here, we present IrRep – a Python code that calculates the symmetry eigenvalues of electronic Bloch states in crystalline solids and the irreducible representations under which they transform. As input it receives bandstructures computed with state-of-the-art Density Functional Theory codes such as VASP, Quantum Espresso, or Abinit, as well as any other code that has an interface to Wannier90. Our code is applicable to materials in any of the 230 space groups and double groups preserving time-reversal symmetry with or without spin-orbit coupling included, for primitive or conventional unit cells. This makes IrRep a powerful tool to systematically analyze the connectivity and topological classification of bands, as well as to detect insulators with non-trivial topology, following the Topological Quantum Chemistry formalism: IrRep can generate the input files needed to calculate the (physical) elementary band representations and the symmetry-based indicators using the [CheckTopologicalMat: https://www.cryst.ehu.es/cgi-bin/cryst/programs/magnetictopo.pl] routine of the Bilbao Crystallographic Server. It is also particularly suitable for interfaces with other plane-waves based codes, due to its flexible structure.
- Authors:
-
- Donostia International Physics Center (DIPC), San Sebastian (Spain); Univ. of the Basque Country (Spain)
- Univ. of the Basque Country (Spain)
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
- Univ. of Zurich (Switzerland)
- Donostia International Physics Center (DIPC), San Sebastian (Spain); Basque Foundation for Science, Bilbao (Spain). IKERBASQUE
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; Spain Ministry of Science and Innovation; National Science Foundation (NSF); Spanish Science Ministry; Basque government; European Union (EU); Swiss National Science Foundation (SNSF)
- OSTI Identifier:
- 1906334
- Grant/Contract Number:
- AC02-05CH11231; PID2019-109905GB-C21; DFG INCIEN2019-000356; DMR-1945058; PGC2018-094626-BC21; IT979-16; PP00P2 176877
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Physics Communications
- Additional Journal Information:
- Journal Volume: 272; Journal ID: ISSN 0010-4655
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; DFT; Symmetry; Irreducible representations; Topology; Python; Bandstructure
Citation Formats
Iraola, Mikel, Mañes, Juan L., Bradlyn, Barry, Horton, Matthew K., Neupert, Titus, Vergniory, Maia G., and Tsirkin, Stepan S. IrRep: Symmetry eigenvalues and irreducible representations of ab initio band structures. United States: N. p., 2021.
Web. doi:10.1016/j.cpc.2021.108226.
Iraola, Mikel, Mañes, Juan L., Bradlyn, Barry, Horton, Matthew K., Neupert, Titus, Vergniory, Maia G., & Tsirkin, Stepan S. IrRep: Symmetry eigenvalues and irreducible representations of ab initio band structures. United States. https://doi.org/10.1016/j.cpc.2021.108226
Iraola, Mikel, Mañes, Juan L., Bradlyn, Barry, Horton, Matthew K., Neupert, Titus, Vergniory, Maia G., and Tsirkin, Stepan S. Tue .
"IrRep: Symmetry eigenvalues and irreducible representations of ab initio band structures". United States. https://doi.org/10.1016/j.cpc.2021.108226. https://www.osti.gov/servlets/purl/1906334.
@article{osti_1906334,
title = {IrRep: Symmetry eigenvalues and irreducible representations of ab initio band structures},
author = {Iraola, Mikel and Mañes, Juan L. and Bradlyn, Barry and Horton, Matthew K. and Neupert, Titus and Vergniory, Maia G. and Tsirkin, Stepan S.},
abstractNote = {Here, we present IrRep – a Python code that calculates the symmetry eigenvalues of electronic Bloch states in crystalline solids and the irreducible representations under which they transform. As input it receives bandstructures computed with state-of-the-art Density Functional Theory codes such as VASP, Quantum Espresso, or Abinit, as well as any other code that has an interface to Wannier90. Our code is applicable to materials in any of the 230 space groups and double groups preserving time-reversal symmetry with or without spin-orbit coupling included, for primitive or conventional unit cells. This makes IrRep a powerful tool to systematically analyze the connectivity and topological classification of bands, as well as to detect insulators with non-trivial topology, following the Topological Quantum Chemistry formalism: IrRep can generate the input files needed to calculate the (physical) elementary band representations and the symmetry-based indicators using the [CheckTopologicalMat: https://www.cryst.ehu.es/cgi-bin/cryst/programs/magnetictopo.pl] routine of the Bilbao Crystallographic Server. It is also particularly suitable for interfaces with other plane-waves based codes, due to its flexible structure.},
doi = {10.1016/j.cpc.2021.108226},
journal = {Computer Physics Communications},
number = ,
volume = 272,
place = {United States},
year = {Tue Nov 16 00:00:00 EST 2021},
month = {Tue Nov 16 00:00:00 EST 2021}
}
Works referenced in this record:
Axionic charge-density wave in the Weyl semimetal (TaSe4)2I
journal, October 2019
- Gooth, J.; Bradlyn, B.; Honnali, S.
- Nature, Vol. 575, Issue 7782
A New Three-Dimensional Subsulfide Ir 2 In 8 S with Dirac Semimetal Behavior
journal, November 2019
- Khoury, Jason F.; Rettie, Alexander J. E.; Khan, Mojammel A.
- Journal of the American Chemical Society, Vol. 141, Issue 48
Graph theory data for topological quantum chemistry
journal, August 2017
- Vergniory, M. G.; Elcoro, L.; Wang, Zhijun
- Physical Review E, Vol. 96, Issue 2
Topological insulators with inversion symmetry
journal, July 2007
- Fu, Liang; Kane, C. L.
- Physical Review B, Vol. 76, Issue 4
Higher-order topological insulators
journal, June 2018
- Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G.
- Science Advances, Vol. 4, Issue 6
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
A complete catalogue of high-quality topological materials
journal, February 2019
- Vergniory, M. G.; Elcoro, L.; Felser, Claudia
- Nature, Vol. 566, Issue 7745
The SIESTA method for ab initio order- N materials simulation
journal, March 2002
- Soler, José M.; Artacho, Emilio; Gale, Julian D.
- Journal of Physics: Condensed Matter, Vol. 14, Issue 11
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
Higher-order topology in bismuth
journal, July 2018
- Schindler, Frank; Wang, Zhijun; Vergniory, Maia G.
- Nature Physics, Vol. 14, Issue 9
Wannier90 as a community code: new features and applications
journal, January 2020
- Pizzi, Giovanni; Vitale, Valerio; Arita, Ryotaro
- Journal of Physics: Condensed Matter, Vol. 32, Issue 16
Directional shift current in mirror-symmetric
journal, March 2020
- Ibañez-Azpiroz, Julen; Souza, Ivo; de Juan, Fernando
- Physical Review Research, Vol. 2, Issue 1
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
Quantitative mappings between symmetry and topology in solids
journal, August 2018
- Song, Zhida; Zhang, Tiantian; Fang, Zhong
- Nature Communications, Vol. 9, Issue 1
Engineering fragile topology in photonic crystals: Topological quantum chemistry of light
journal, October 2019
- de Paz, María Blanco; Vergniory, Maia G.; Bercioux, Dario
- Physical Review Research, Vol. 1, Issue 3
Efficient topological materials discovery using symmetry indicators
journal, February 2019
- Tang, Feng; Po, Hoi Chun; Vishwanath, Ashvin
- Nature Physics, Vol. 15, Issue 5
Topological Crystalline Insulators
journal, March 2011
- Fu, Liang
- Physical Review Letters, Vol. 106, Issue 10
Recent developments in the ABINIT software package
journal, August 2016
- Gonze, X.; Jollet, F.; Abreu Araujo, F.
- Computer Physics Communications, Vol. 205
The Subchalcogenides Ir 2 In 8 Q (Q = S, Se, Te): Dirac Semimetal Candidates with Re-entrant Structural Modulation
journal, March 2020
- Khoury, Jason F.; Rettie, Alexander J. E.; Robredo, Iñigo
- Journal of the American Chemical Society, Vol. 142, Issue 13
Spectral and optical properties of Ag 3 Au(Se 2 ,Te 2 ) and dark matter detection
journal, October 2019
- Sánchez-Martínez, M-Á; Robredo, I.; Bidaurrazaga, A.
- Journal of Physics: Materials, Vol. 3, Issue 1
Topological quantum chemistry
journal, July 2017
- Bradlyn, Barry; Elcoro, L.; Cano, Jennifer
- Nature, Vol. 547, Issue 7663
Band representations and symmetry types of bands in solids
journal, March 1981
- Zak, J.
- Physical Review B, Vol. 23, Issue 6
Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals
journal, July 1936
- Bouckaert, L. P.; Smoluchowski, R.; Wigner, E.
- Physical Review, Vol. 50, Issue 1
Three-Dimensional Antiferromagnetic Order and AnisotropicMagnetic Properties in Bi 2 CuO 4
journal, July 1991
- Yamada, Kazuyoshi; Takada, Ken-ichi; Hosoya, Syoichi
- Journal of the Physical Society of Japan, Vol. 60, Issue 7
Symmetry Specification of Bands in Solids
journal, September 1980
- Zak, J.
- Physical Review Letters, Vol. 45, Issue 12
Symmetry-based indicators of band topology in the 230 space groups
journal, June 2017
- Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki
- Nature Communications, Vol. 8, Issue 1
Topological crystalline insulators in the SnTe material class
journal, January 2012
- Hsieh, Timothy H.; Lin, Hsin; Liu, Junwei
- Nature Communications, Vol. 3, Article No. 982
Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
journal, July 2016
- Bradlyn, Barry; Cano, Jennifer; Wang, Zhijun
- Science, Vol. 353, Issue 6299
Topological invariants of time-reversal-invariant band structures
journal, March 2007
- Moore, J. E.; Balents, L.
- Physical Review B, Vol. 75, Issue 12, Article No. 121306(R)
Implementation of the projector augmented-wave method in the ABINIT code: Application to the study of iron under pressure
journal, April 2008
- Torrent, Marc; Jollet, François; Bottin, François
- Computational Materials Science, Vol. 42, Issue 2
Catalogue of topological electronic materials
journal, February 2019
- Zhang, Tiantian; Jiang, Yi; Song, Zhida
- Nature, Vol. 566, Issue 7745
Symmetry indicators of band topology
journal, April 2020
- Po, Hoi Chun
- Journal of Physics: Condensed Matter, Vol. 32, Issue 26
Entanglement and inversion symmetry in topological insulators
journal, December 2010
- Turner, Ari M.; Zhang, Yi; Vishwanath, Ashvin
- Physical Review B, Vol. 82, Issue 24
Strong and fragile topological Dirac semimetals with higher-order Fermi arcs
journal, January 2020
- Wieder, Benjamin J.; Wang, Zhijun; Cano, Jennifer
- Nature Communications, Vol. 11, Issue 1
The Subchalcogenides Ir 2 In 8 Q (Q = S, Se, Te): Dirac Semimetal Candidates with Re-entrant Structural Modulation
journal, March 2020
- Khoury, Jason F.; Rettie, Alexander J. E.; Robredo, Iñigo
- Journal of the American Chemical Society, Vol. 142, Issue 13
A New Three-Dimensional Subsulfide Ir 2 In 8 S with Dirac Semimetal Behavior
journal, November 2019
- Khoury, Jason F.; Rettie, Alexander J. E.; Khan, Mojammel A.
- Journal of the American Chemical Society, Vol. 141, Issue 48
Higher-order topology in bismuth
journal, July 2018
- Schindler, Frank; Wang, Zhijun; Vergniory, Maia G.
- Nature Physics, Vol. 14, Issue 9
A complete catalogue of high-quality topological materials
journal, February 2019
- Vergniory, M. G.; Elcoro, L.; Felser, Claudia
- Nature, Vol. 566, Issue 7745
Composite Weyl nodes stabilized by screw symmetry with and without time-reversal invariance
journal, July 2017
- Tsirkin, Stepan S.; Souza, Ivo; Vanderbilt, David
- Physical Review B, Vol. 96, Issue 4
Band connectivity for topological quantum chemistry: Band structures as a graph theory problem
journal, January 2018
- Bradlyn, Barry; Elcoro, L.; Vergniory, M. G.
- Physical Review B, Vol. 97, Issue 3
Disconnected elementary band representations, fragile topology, and Wilson loops as topological indices: An example on the triangular lattice
journal, January 2019
- Bradlyn, Barry; Wang, Zhijun; Cano, Jennifer
- Physical Review B, Vol. 99, Issue 4
Higher-order and crystalline topology in a phenomenological tight-binding model of lead telluride
journal, April 2019
- Robredo, Iñigo; Vergniory, Maia G.; Bradlyn, Barry
- Physical Review Materials, Vol. 3, Issue 4
Fractional corner charges in spin-orbit coupled crystals
journal, November 2019
- Schindler, Frank; Brzezińska, Marta; Benalcazar, Wladimir A.
- Physical Review Research, Vol. 1, Issue 3
Double crystallographic groups and their representations on the Bilbao Crystallographic Server
text, January 2017
- Elcoro, Luis; Bradlyn, Barry; Wang, Zhijun
- arXiv
Higher-Order Topological Insulators
text, January 2017
- Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G.
- arXiv
Evidence for an axionic charge density wave in the Weyl semimetal (TaSe4)2I
text, January 2019
- Gooth, Johannes; Bradlyn, Barry; Honnali, Shashank
- arXiv
Works referencing / citing this record:
Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light
journal, December 2021
- Rodriguez-Vega, Martin; Vogl, Michael; Fiete, Gregory A.
- Physical Review B, Vol. 104, Issue 24