skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials


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: 95; Journal Issue: 7; Journal ID: ISSN 2469-9950
American Physical Society (APS)
Country of Publication:
United States
Materials Science; Physics

Citation Formats

Gresch, Dominik, Autès, Gabriel, Yazyev, Oleg V., Troyer, Matthias, Vanderbilt, David, Bernevig, B. Andrei, and Soluyanov, Alexey A. Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials. United States: N. p., 2017. Web. doi:10.1103/physrevb.95.075146.
Gresch, Dominik, Autès, Gabriel, Yazyev, Oleg V., Troyer, Matthias, Vanderbilt, David, Bernevig, B. Andrei, & Soluyanov, Alexey A. Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials. United States. doi:10.1103/physrevb.95.075146.
Gresch, Dominik, Autès, Gabriel, Yazyev, Oleg V., Troyer, Matthias, Vanderbilt, David, Bernevig, B. Andrei, and Soluyanov, Alexey A. Wed . "Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials". United States. doi:10.1103/physrevb.95.075146.
title = {Z2Pack: Numerical implementation of hybrid Wannier centers for identifying topological materials},
author = {Gresch, Dominik and Autès, Gabriel and Yazyev, Oleg V. and Troyer, Matthias and Vanderbilt, David and Bernevig, B. Andrei and Soluyanov, Alexey A.},
abstractNote = {Not provided.},
doi = {10.1103/physrevb.95.075146},
journal = {Physical Review B},
issn = {2469-9950},
number = 7,
volume = 95,
place = {United States},
year = {2017},
month = {2}

Works referenced in this record:

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

Colloquium: Topological insulators
journal, November 2010

Topological insulators and superconductors
journal, October 2011

Classification of topological insulators and superconductors in three spatial dimensions
journal, November 2008

Quantum Spin Hall Effect in Graphene
journal, November 2005

Topological Insulators in Three Dimensions
journal, March 2007

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

Z2classification of quantum spin Hall systems: An approach using time-reversal invariance
journal, May 2009

Topological phases and the quantum spin Hall effect in three dimensions
journal, May 2009

Antiferromagnetic topological insulators
journal, June 2010

Topological insulators with commensurate antiferromagnetism
journal, August 2013

Topological Crystalline Insulators
journal, March 2011

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

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

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

Wannier center sheets in topological insulators
journal, March 2014

Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988

Quantized Hall Conductance in a Two-Dimensional Periodic Potential
journal, August 1982

Topological invariant and the quantization of the Hall conductance
journal, April 1985

Topological field theory of time-reversal invariant insulators
journal, November 2008

  • Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng
  • Physical Review B, Vol. 78, Issue 19, Article No. 195424
  • DOI: 10.1103/PhysRevB.78.195424

Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators
journal, April 2009

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

  • Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C.
  • Science, Vol. 314, Issue 5806, p. 1757-1761
  • DOI: 10.1126/science.1133734

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

Unpaired Majorana fermions in quantum wires
journal, October 2001

Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator
journal, March 2008

Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
journal, August 2010

Helical Liquids and Majorana Bound States in Quantum Wires
journal, October 2010

Majorana fermions in a tunable semiconductor device
journal, March 2010

Fault-tolerant quantum computation by anyons
journal, January 2003

Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
journal, November 2004

The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal
journal, November 1983

Weyl Semimetal in a Topological Insulator Multilayer
journal, September 2011

Topological nodal semimetals
journal, December 2011

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

Adler-Bell-Jackiw anomaly in Weyl semimetals: Application to pyrochlore iridates
journal, June 2012

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

  • Ali, Mazhar N.; Xiong, Jun; Flynn, Steven
  • Nature, Vol. 514, Issue 7521
  • DOI: 10.1038/nature13763

Chiral anomaly and classical negative magnetoresistance of Weyl metals
journal, September 2013

Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs
journal, August 2015

Experimental Discovery of Weyl Semimetal TaAs
journal, July 2015

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

  • Liang, Tian; Gibson, Quinn; Ali, Mazhar N.
  • Nature Materials, Vol. 14, Issue 3
  • DOI: 10.1038/nmat4143

Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe
journal, August 2015

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

  • Zhang, Haijun; Liu, Chao-Xing; Qi, Xiao-Liang
  • Nature Physics, Vol. 5, Issue 6, p. 438-442
  • DOI: 10.1038/nphys1270

Helical edge and surface states in HgTe quantum wells and bulk insulators
journal, March 2008

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

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

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

  • Hsieh, D.; Qian, D.; Wray, L.
  • Nature, Vol. 452, Issue 7190, p. 970-974
  • DOI: 10.1038/nature06843

Observation of Unconventional Quantum Spin Textures in Topological Insulators
journal, February 2009

Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
journal, May 2009

  • Xia, Y.; Qian, D.; Hsieh, D.
  • Nature Physics, Vol. 5, Issue 6, p. 398-402
  • DOI: 10.1038/nphys1274

Half-Heusler Compounds as a New Class of Three-Dimensional Topological Insulators
journal, August 2010

Three-Dimensional Topological Insulators in I III VI 2 and II IV V 2 Chalcopyrite Semiconductors
journal, January 2011

Localized edge states in two-dimensional topological insulators: Ultrathin Bi films
journal, March 2011

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

  • Neupane, Madhab; Xu, Su-Yang; Sankar, Raman
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms4786

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

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

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

  • Liu, Z. K.; Jiang, J.; Zhou, B.
  • Nature Materials, Vol. 13, Issue 7
  • DOI: 10.1038/nmat3990

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
journal, January 2014

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

Electron localization in the insulating state: Application to crystalline semiconductors
journal, August 2001

Electric Polarization in a Chern Insulator
journal, March 2009

Wannier representation of Z 2 topological insulators
journal, January 2011

Computing topological invariants without inversion symmetry
journal, June 2011

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

Wilson-loop characterization of inversion-symmetric topological insulators
journal, April 2014

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

Type-II Weyl semimetals
journal, November 2015

  • Soluyanov, Alexey A.; Gresch, Dominik; Wang, Zhijun
  • Nature, Vol. 527, Issue 7579
  • DOI: 10.1038/nature15768

MoTe 2 : A Type-II Weyl Topological Metal
journal, July 2016

Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides X P 2 ( X = Mo , W)
journal, August 2016

Nodal-chain metals
journal, August 2016

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

Triple Point Topological Metals
journal, July 2016

Topological Nonsymmorphic Metals from Band Inversion
journal, December 2016

Maximally localized generalized Wannier functions for composite energy bands
journal, November 1997

Wannier functions for magnetic sub-bands
journal, April 1984

Exponential Localization of Wannier Functions in Insulators
journal, January 2007

Bloch Bundles, Marzari-Vanderbilt Functional and Maximally Localized Wannier Functions
journal, June 2013

  • Panati, Gianluca; Pisante, Adriano
  • Communications in Mathematical Physics, Vol. 322, Issue 3
  • DOI: 10.1007/s00220-013-1741-y

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

Theory of polarization of crystalline solids
journal, January 1993

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

Quantization of particle transport
journal, May 1983

Appearance of Gauge Structure in Simple Dynamical Systems
journal, June 1984

Characteristic Classes of Hermitian Manifolds
journal, January 1946

  • Chern, Shiing-shen
  • The Annals of Mathematics, Vol. 47, Issue 1
  • DOI: 10.2307/1969037

Smooth gauge for topological insulators
journal, March 2012

Non-commutative tools for topological insulators
journal, June 2010

Time reversal polarization and a Z 2 adiabatic spin pump
journal, November 2006

Quantum Anomalous Hall Effect in Hg 1 y Mn y Te Quantum Wells
journal, October 2008

Quantum anomalous Hall effect in graphene from Rashba and exchange effects
journal, October 2010

Quantized Anomalous Hall Effect in Magnetic Topological Insulators
journal, June 2010

Magnetically doped semiconducting topological insulators
journal, September 2012

  • Kou, X. F.; Jiang, W. J.; Lang, M. R.
  • Journal of Applied Physics, Vol. 112, Issue 6
  • DOI: 10.1063/1.4754452

Hedgehog spin texture and Berry’s phase tuning in a magnetic topological insulator
journal, June 2012

  • Xu, Su-Yang; Neupane, Madhab; Liu, Chang
  • Nature Physics, Vol. 8, Issue 8
  • DOI: 10.1038/nphys2351

Quantum anomalous Hall effect in doped ternary chalcogenide topological insulators TlBiTe 2 and TlBiSe 2
journal, October 2011

  • Niu, Chengwang; Dai, Ying; Yu, Lin
  • Applied Physics Letters, Vol. 99, Issue 14
  • DOI: 10.1063/1.3645624

Quantum anomalous Hall effect with tunable Chern number in magnetic topological insulator film
journal, January 2012

Engineering quantum anomalous Hall phases with orbital and spin degrees of freedom
journal, May 2013

Chern Insulators from Heavy Atoms on Magnetic Substrates
journal, March 2013

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
journal, March 2013

A new mixing of Hartree–Fock and local density‐functional theories
journal, January 1993

  • Becke, Axel D.
  • The Journal of Chemical Physics, Vol. 98, Issue 2
  • DOI: 10.1063/1.464304

Toward reliable density functional methods without adjustable parameters: The PBE0 model
journal, April 1999

  • Adamo, Carlo; Barone, Vincenzo
  • The Journal of Chemical Physics, Vol. 110, Issue 13
  • DOI: 10.1063/1.478522

Hybrid functionals based on a screened Coulomb potential
journal, May 2003

  • Heyd, Jochen; Scuseria, Gustavo E.; Ernzerhof, Matthias
  • The Journal of Chemical Physics, Vol. 118, Issue 18
  • DOI: 10.1063/1.1564060

The GW method
journal, March 1998

Possible States for a Three-Dimensional Electron Gas in a Strong Magnetic Field
journal, January 1987

Disordered topological insulators via C * -algebras
journal, December 2010

Quantum Spin-Hall Effect and Topologically Invariant Chern Numbers
journal, July 2006

Robustness of the spin-Chern number
journal, September 2009

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Projector augmented-wave method
journal, December 1994

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

X-ray Diffraction and 119 Sn Mössbauer Spectroscopy Study of a New Phase in the Bi 2 Se 3 −SnSe System:  SnBi 4 Se 7
journal, May 1999

  • Pérez Vicente, C.; Tirado, J. L.; Adouby, K.
  • Inorganic Chemistry, Vol. 38, Issue 9
  • DOI: 10.1021/ic9812858

Topological insulators with inversion symmetry
journal, July 2007

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
  • DOI: 10.1038/ncomms1969

Experimental realization of a topological crystalline insulator in SnTe
journal, September 2012

  • Tanaka, Y.; Ren, Zhi; Sato, T.
  • Nature Physics, Vol. 8, Issue 11
  • DOI: 10.1038/nphys2442

Inhomogeneous Electron Gas
journal, November 1964

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965

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

Spin-orbit coupling with ultrasoft pseudopotentials: Application to Au and Pt
journal, March 2005

Lattice dynamics and structure of GeTe, SnTe and PbTe
journal, December 2012

  • Bauer Pereira, Paula; Sergueev, Ilya; Gorsse, Stéphane
  • physica status solidi (b), Vol. 250, Issue 7
  • DOI: 10.1002/pssb.201248412

Adiabatic Pumping of Chern-Simons Axion Coupling
journal, March 2015

wannier90: A tool for obtaining maximally-localised Wannier functions
journal, May 2008

  • Mostofi, Arash A.; Yates, Jonathan R.; Lee, Young-Su
  • Computer Physics Communications, Vol. 178, Issue 9
  • DOI: 10.1016/j.cpc.2007.11.016

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

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

  • Jeon, Sangjun; Zhou, Brian B.; Gyenis, Andras
  • Nature Materials, Vol. 13, Issue 9
  • DOI: 10.1038/nmat4023

On the Arsenides and Antimonides of Tantalum.
journal, January 1965

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

Fermions with cubic and quartic spectrum
journal, November 2010

Experimental observation of Weyl points
journal, July 2015

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

  • Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8373

Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides
journal, March 2015

Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969

A PCAC puzzle: π0→γγ in the σ-model
journal, March 1969

Quantum magnetoresistance
journal, August 1998

Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP
journal, May 2016

  • Arnold, Frank; Shekhar, Chandra; Wu, Shu-Chun
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms11615

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

Topological Phases in InAs 1 x Sb x : From Novel Topological Semimetal to Majorana Wire
journal, August 2016

Double Dirac Semimetals in Three Dimensions
journal, May 2016

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

Chern Semimetal and the Quantized Anomalous Hall Effect in HgCr 2 Se 4
journal, October 2011

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

ABINIT: First-principles approach to material and nanosystem properties
journal, December 2009

Matplotlib: A 2D Graphics Environment
journal, January 2007

Proposal for Direct Measurement of Topological Invariants in Optical Lattices
journal, April 2013

Measuring Z 2 topological invariants in optical lattices using interferometry
journal, April 2014

An Aharonov-Bohm interferometer for determining Bloch band topology
journal, December 2014

Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions
journal, January 2016

Normal Form of Antiunitary Operators
journal, September 1960

  • Wigner, Eugene P.
  • Journal of Mathematical Physics, Vol. 1, Issue 5
  • DOI: 10.1063/1.1703672