Colloquium : Topological band theory

Bansil, A.; Lin, Hsin; Das, Tanmoy

doi:10.1103/RevModPhys.88.021004

Title: Colloquium : Topological band theory

Abstract

The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. We begin this review by discussing underpinnings of the topological band theory, which basically involves a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder/interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary and quaternary compounds, transition metal and f-electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultra-thin filmsmore »« less

Authors:

Bansil, A. ^[1]; Lin, Hsin ^[2]; Das, Tanmoy ^[3]

Northeastern Univ., Boston, MA (United States)
Northeastern Univ., Boston, MA (United States); National Univ. of Singapore (Singapore)
National Univ. of Singapore (Singapore); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Wed Jun 29 00:00:00 EDT 2016

Research Org.:: Energy Frontier Research Centers (EFRC) (United States). Center for the Computational Design of Functional Layered Materials (CCDM)

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

OSTI Identifier:: 1371106

Alternate Identifier(s):: OSTI ID: 1259904

Grant/Contract Number:: SC0012575; FG02-07ER46352; AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Reviews of Modern Physics

Additional Journal Information:: Journal Volume: 88; Journal Issue: 2; Related Information: CCDM partners with Temple University (lead); Brookhaven National Laboratory; Drexel University; Duke University; North Carolina State University; Northeastern University; Princeton University; Rice University; University of Pennsylvania; Journal ID: ISSN 0034-6861

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; catalysis (heterogeneous); solar (photovoltaic); energy storage (including batteries and capacitors); hydrogen and fuel cells; defects; mechanical behavior; materials and chemistry by design; synthesis (novel materials)

Citation Formats


                    Bansil, A., Lin, Hsin, and Das, Tanmoy. Colloquium : Topological band theory.  United States: N. p., 2016. 
Web.  doi:10.1103/RevModPhys.88.021004.

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                    Bansil, A., Lin, Hsin, & Das, Tanmoy. Colloquium : Topological band theory.  United States.  https://doi.org/10.1103/RevModPhys.88.021004

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                    Bansil, A., Lin, Hsin, and Das, Tanmoy. Wed .  
"Colloquium : Topological band theory".  United States.  https://doi.org/10.1103/RevModPhys.88.021004.  https://www.osti.gov/servlets/purl/1371106.

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@article{osti_1371106,

  title        = {Colloquium : Topological band theory},

  author       = {Bansil, A. and Lin, Hsin and Das, Tanmoy},

  abstractNote = {The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling direct and sharpened confrontation between theory and experiment. We begin this review by discussing underpinnings of the topological band theory, which basically involves a layer of analysis and interpretation for assessing topological properties of band structures beyond the standard band theory construct. Methods for evaluating topological invariants are delineated, including crystals without inversion symmetry and interacting systems. The extent to which theoretically predicted properties and protections of topological states have been verified experimentally is discussed, including work on topological crystalline insulators, disorder/interaction driven topological insulators (TIs), topological superconductors, Weyl semimetal phases, and topological phase transitions. Successful strategies for new materials discovery process are outlined. A comprehensive survey of currently predicted 2D and 3D topological materials is provided. This includes binary, ternary and quaternary compounds, transition metal and f-electron materials, Weyl and 3D Dirac semimetals, complex oxides, organometallics, skutterudites and antiperovskites. Also included is the emerging area of 2D atomically thin films beyond graphene of various elements and their alloys, functional thin films, multilayer systems, and ultra-thin films of 3D TIs, all of which hold exciting promise of wide-ranging applications. We conclude by giving a perspective on research directions where further work will broadly benefit the topological materials field},

  doi          = {10.1103/RevModPhys.88.021004},

  journal      = {Reviews of Modern Physics},

  number       = 2,

  volume       = 88,

  place        = {United States},

  year         = {Wed Jun 29 00:00:00 EDT 2016},

  month        = {Wed Jun 29 00:00:00 EDT 2016}

}

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DOI: 10.1088/2399-6528/ab5872

Non-Bloch topological invariants in a non-Hermitian domain wall system
journal, July 2019

Deng, Tian-Shu; Yi, Wei
Physical Review B, Vol. 100, Issue 3
DOI: 10.1103/physrevb.100.035102

Magnetization-governed magnetoresistance anisotropy in the topological semimetal CeBi
journal, November 2019

Lyu, Yang-Yang; Han, Fei; Xiao, Zhi-Li
Physical Review B, Vol. 100, Issue 18
DOI: 10.1103/physrevb.100.180407

Quasi-two-dimensional massless Dirac fermions in ${CaMnSb}_{2}$
journal, January 2017

He, J. B.; Fu, Y.; Zhao, L. X.
Physical Review B, Vol. 95, Issue 4
DOI: 10.1103/physrevb.95.045128

Nodal loop and nodal surface states in the ${Ti}_{3} Al$ family of materials
journal, June 2018

Zhang, Xiaoming; Yu, Zhi-Ming; Zhu, Ziming
Physical Review B, Vol. 97, Issue 23
DOI: 10.1103/physrevb.97.235150

Finite-size effects in non-Hermitian topological systems
journal, April 2019

Chen, Rui; Chen, Chui-Zhen; Zhou, Bin
Physical Review B, Vol. 99, Issue 15
DOI: 10.1103/physrevb.99.155431

Non-Hermitian Sonic Second-Order Topological Insulator
journal, May 2019

Zhang, Zhiwang; Rosendo López, María; Cheng, Ying
Physical Review Letters, Vol. 122, Issue 19
DOI: 10.1103/physrevlett.122.195501

Review of Electron-Electron Interaction Effects in Planar Dirac Liquids
journal, August 2019

Teber, S.; Kotikov, A. V.
Theoretical and Mathematical Physics, Vol. 200, Issue 2
DOI: 10.1134/s0040577919080130

Spoof Plasmonics: From Metamaterial Concept to Topological Description
journal, May 2018

Gao, Zhen; Wu, Lin; Gao, Fei
Advanced Materials, Vol. 30, Issue 31
DOI: 10.1002/adma.201706683

New topological invariants in non-Hermitian systems
journal, April 2019

Ghatak, Ananya; Das, Tanmoy
Journal of Physics: Condensed Matter, Vol. 31, Issue 26
DOI: 10.1088/1361-648x/ab11b3

$Z_{2}$ topological quantum paramagnet on a honeycomb bilayer
journal, July 2019

Joshi, Darshan G.; Schnyder, Andreas P.
Physical Review B, Vol. 100, Issue 2
DOI: 10.1103/physrevb.100.020407

Tunable skyrmion-skyrmion binding on the surface of a topological insulator
journal, September 2019

Tiwari, Kunal L.; Lavoie, J.; Pereg-Barnea, T.
Physical Review B, Vol. 100, Issue 12
DOI: 10.1103/physrevb.100.125414

Hall conductance of a non-Hermitian Chern insulator
journal, December 2018

Chen, Yu; Zhai, Hui
Physical Review B, Vol. 98, Issue 24
DOI: 10.1103/physrevb.98.245130

Symmetry-protected nodal phases in non-Hermitian systems
journal, January 2019

Budich, Jan Carl; Carlström, Johan; Kunst, Flore K.
Physical Review B, Vol. 99, Issue 4
DOI: 10.1103/physrevb.99.041406

Probing non-Hermitian skin effect and non-Bloch phase transitions
journal, September 2019

Longhi, Stefano
Physical Review Research, Vol. 1, Issue 2
DOI: 10.1103/physrevresearch.1.023013

Magnetism and anomalous transport in the Weyl semimetal PrAlGe: possible route to axial gauge fields
text, January 2020

Destraz, Daniel; Das, Lakshmi; Tsirkin, Stepan S.
Nature Publishing Group
DOI: 10.5167/uzh-182396

Tunable double-Weyl Fermion semimetal state in the SrSi2 materials class
journal, July 2018

Singh, Bahadur; Chang, Guoqing; Chang, Tay-Rong
Scientific Reports, Vol. 8, Issue 1
DOI: 10.1038/s41598-018-28644-y

Fundamental insights to topological quantum materials: A real-space view of 13 cases by supersymmetry of valence bonds approach
journal, March 2019

Chou, Fang-Cheng
Applied Physics Reviews, Vol. 6, Issue 1
DOI: 10.1063/1.5066031

First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials
journal, February 2020

Poncé, Samuel; Li, Wenbin; Reichardt, Sven
Reports on Progress in Physics, Vol. 83, Issue 3
DOI: 10.1088/1361-6633/ab6a43

Dynamical polarization in a graphene-topological-insulator heterostructure
journal, January 2019

Zuber, Jack; Huang, Sunchao; Tian, Jie
Materials Research Express, Vol. 6, Issue 4
DOI: 10.1088/2053-1591/aaf998

Magnetically controllable topological quantum phase transitions in the antiferromagnetic topological insulator ${MnBi}_{2} {Te}_{4}$
journal, September 2019

Li, Jiaheng; Wang, Chong; Zhang, Zetao
Physical Review B, Vol. 100, Issue 12
DOI: 10.1103/physrevb.100.121103

Phase diagrams in materials science of topological insulators based on metal chalcogenides
journal, December 2017

Babanly, M. B.; Chulkov, E. V.; Aliev, Z. S.
Russian Journal of Inorganic Chemistry, Vol. 62, Issue 13
DOI: 10.1134/s0036023617130034

Topological Phononics: From Fundamental Models to Real Materials
journal, August 2019

Liu, Yizhou; Chen, Xiaobin; Xu, Yong
Advanced Functional Materials, Vol. 30, Issue 8
DOI: 10.1002/adfm.201904784

Recent Advances in van der Waals Heterojunctions Based on Semiconducting Transition Metal Dichalcogenides
journal, August 2018

Li, Ruiping; Li, Lain‐Jong; Cheng, Yingchun
Advanced Electronic Materials, Vol. 4, Issue 11
DOI: 10.1002/aelm.201800270

Synthesis and chemistry of elemental 2D materials
journal, January 2017

Mannix, Andrew J.; Kiraly, Brian; Hersam, Mark C.
Nature Reviews Chemistry, Vol. 1, Issue 2
DOI: 10.1038/s41570-016-0014

A methodical study of quantum phase engineering in topological crystalline insulator SnTe and related alloys
journal, January 2019

Yarmohammadi, Mohsen; Mirabbaszadeh, Kavoos
Physical Chemistry Chemical Physics, Vol. 21, Issue 38
DOI: 10.1039/c9cp03655e

Highly anisotropic type-II nodal line state in pure titanium metal
journal, March 2018

Zhang, Xiaoming; Jin, Lei; Dai, Xuefang
Applied Physics Letters, Vol. 112, Issue 12
DOI: 10.1063/1.5023320

Josephson signatures of Weyl node creation and annihilation in irradiated Dirac semimetals
journal, September 2019

Fu, Pei-Hao; Wang, Jun; Liu, Jun-Feng
Physical Review B, Vol. 100, Issue 11
DOI: 10.1103/physrevb.100.115414

Topological crystalline insulator state with type-II Dirac fermions in transition metal dipnictides
journal, November 2019

Wang, Baokai; Singh, Bahadur; Ghosh, Barun
Physical Review B, Vol. 100, Issue 20
DOI: 10.1103/physrevb.100.205118

Topological transitions in a model for proximity-induced superconductivity
journal, December 2019

Batra, Navketan; Nayak, Swagatam; Kumar, Sanjeev
Physical Review B, Vol. 100, Issue 21
DOI: 10.1103/physrevb.100.214517

Dynamical topological invariant after a quantum quench
journal, February 2018

Yang, Chao; Li, Linhu; Chen, Shu
Physical Review B, Vol. 97, Issue 6
DOI: 10.1103/physrevb.97.060304

Nodal-link semimetals
text, January 2017

Yan, Zhongbo; Bi, Ren; Shen, Huitao
arXiv
DOI: 10.48550/arxiv.1704.00655

All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions
text, January 2019

Kadek, Marius; Repisky, Michal; Ruud, Kenneth
arXiv
DOI: 10.48550/arxiv.1902.02828

Non-Hermitian topology of spontaneous magnon decay
text, January 2019

McClarty, Paul A.; Rau, Jeffrey G.
arXiv
DOI: 10.48550/arxiv.1904.02160

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Title: Colloquium : Topological band theory

Abstract

Citation Formats

d-Band filling in Ni-P metallic glasses journal, July 1985

Probing the Fermi surface of three-dimensional Dirac semimetal Cd 3 As 2 through the de Haas–van Alphen technique journal, April 2015

One-Dimensional Edge States with Giant Spin Splitting in a Bismuth Thin Film journal, February 2015

Dirac materials journal, January 2014

Surface and bulk electronic structure of the strongly correlated system SmB 6 and implications for a topological Kondo insulator journal, September 2013

Quantum spin Hall effect in a disordered hexagonal Si x Ge 1 − x alloy journal, November 2013

Quantized hall effect in superfluid helium-3 film journal, April 1988

d + i d ′ Chiral Superconductivity in Bilayer Silicene journal, August 2013

Floquet topological insulator in semiconductor quantum wells journal, March 2011

Tailoring Magnetic Doping in the Topological Insulator Bi 2 Se 3 journal, December 2012

Rocksalt SnS and SnSe: Native topological crystalline insulators journal, December 2013

Creation of helical Dirac fermions by interfacing two gapped systems of ordinary fermions journal, January 2013

Topological-Metal to Band-Insulator Transition in ( Bi 1 − x In x ) 2 Se 3 Thin Films journal, October 2012

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

UPt 3 as a Topological Crystalline Superconductor journal, November 2013

First-principles investigations of the atomic, electronic, and thermoelectric properties of equilibrium and strained Bi 2 Se 3 and Bi 2 Te 3 including van der Waals interactions journal, November 2012

Making Massless Dirac Fermions from a Patterned Two-Dimensional Electron Gas journal, May 2009

Persistence of a Two-Dimensional Topological Insulator State in Wide HgTe Quantum Wells journal, March 2015

Topological Insulator Bi2Se3 Nanowire High Performance Field-Effect Transistors journal, April 2013

Topological insulators in the quaternary chalcogenide compounds and ternary famatinite compounds journal, August 2011

Theoretical prediction of topological insulator in ternary rare earth chalcogenides journal, October 2010

Stable Nontrivial Z 2 Topology in Ultrathin Bi (111) Films: A First-Principles Study journal, September 2011

Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors journal, August 2006

Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator journal, March 2011

The electronic properties of graphene journal, January 2009

Topological electronic structure and Weyl semimetal in the TlBiSe 2 class of semiconductors journal, September 2012

Topological phase transition in bulk materials described by the coherent potential approximation technique journal, October 2012

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi 2 Se 3 journal, March 2014

Superconductivity near 30 K without copper: the Ba0.6K0.4BiO3 perovskite journal, April 1988

Electronic Momentum Densities by Two-Dimensional Angular Correlation of Annihilation Radiation in Aluminum journal, November 1976

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates journal, August 2011

Observation of Surface Dirac Cone in High-Quality Ultrathin Epitaxial Bi 2 Se 3 Topological Insulator on AlN(0001) Dielectric journal, June 2014

Weak topological insulators induced by the interlayer coupling: A first-principles study of stacked Bi 2 TeI journal, January 2014

Positron studies of metallic YBa2Cu3O7−x journal, January 1991

Absence of helical surface states in bulk semimetals with broken inversion symmetry journal, March 2014

Materials science: Enter the oxides journal, May 2009

Magnetic pyrochlore oxides journal, January 2010

Dirac semimetals A 3 Bi ( A = Na , K , Rb ) as Z 2 Weyl semimetals journal, March 2015

Colloquium : Andreev reflection and Klein tunneling in graphene journal, October 2008

Floquet chiral edge states in graphene journal, March 2014

Topological insulators with inversion symmetry journal, July 2007

Coherent-potential and average t -matrix approximations for disordered muffin-tin alloys. II. Application to realistic systems journal, November 1979

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

Intermediate coupling model of the cuprates journal, May 2014

Ultrafast helicity control of surface currents in topological insulators with near-unity fidelity journal, March 2015

Surface Scattering via Bulk Continuum States in the 3D Topological Insulator Bi 2 Se 3 journal, July 2011

Quantum Spin Hall Effect in Graphene journal, November 2005

Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi 2 Te 3 and Sb 2 Te 3 journal, September 2009

Quantum Spin Hall Effect in Inverted Type-II Semiconductors journal, June 2008

Electronic structure of the quantum spin Hall parent compound CdTe and related topological issues journal, November 2014

Topological Oxide Insulator in Cubic Perovskite Structure journal, April 2013

Dual-Gated Topological Insulator Thin-Film Device for Efficient Fermi-Level Tuning journal, February 2015

Quantal Phase Factors Accompanying Adiabatic Changes journal, March 1984

Topological edge states and electronic structures of a 2D topological insulator: Single-bilayer Bi (111) journal, June 2013

Emergent quantum confinement at topological insulator surfaces journal, January 2012

Vibrations in binary and ternary topological insulators: First-principles calculations and Raman spectroscopy measurements journal, November 2012

Pressure-induced topological insulating behavior in the ternary chalcogenide Ge 2 Sb 2 Te 5 journal, August 2011

Probing the Electronic Properties of Individual MnPc Molecules Coupled to Topological States journal, August 2014

Magnetic proximity effect at the three-dimensional topological insulator/magnetic insulator interface journal, October 2013

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

Design Principles and Coupling Mechanisms in the 2D Quantum Well Topological Insulator HgTe / CdTe journal, October 2010

Possible high-temperature superconducting state with a d + i d pairing symmetry in doped graphene journal, February 2010

Topological semimetal in a Bi-Bi 2 Se 3 infinitely adaptive superlattice phase journal, December 2012

Temperature-Induced Coexistence of a Conducting Bilayer and the Bulk-Terminated Surface of the Topological Insulator Bi 2 Te 3 journal, August 2013

Engineering the quantum anomalous Hall effect in graphene with uniaxial strains journal, December 2013

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

Coherent-potential and average t -matrix approximations for disordered muffin-tin alloys. I. Formalism journal, November 1979

Tunable topological electronic structures in Sb(111) bilayers: A first-principles study journal, January 2013

Strain-driven onset of nontrivial topological insulating states in Zintl Sr 2 X compounds ( X = Pb , Sn) journal, October 2011

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

Fundamental Optical Absorption in β -Silver Telluride journal, February 1966

Single Crystalline Nanostructures of Topological Crystalline Insulator SnTe with Distinct Facets and Morphologies journal, October 2013

Topological Properties Determined by Atomic Buckling in Self-Assembled Ultrathin Bi(110) journal, December 2014

Floquet Spectrum and Transport through an Irradiated Graphene Ribbon journal, November 2011

Ripple-modulated electronic structure of a 3D topological insulator journal, January 2012

Evolution of Midgap States and Residual Three Dimensionality in La 2 − x Sr x CuO 4 journal, October 2005

Terahertz Response and Colossal Kerr Rotation from the Surface States of the Topological Insulator Bi 2 Se 3 journal, February 2012

d-Band filling in Ni-P metallic glasses
journal, July 1985

Probing the Fermi surface of three-dimensional Dirac semimetal ${Cd}_{3} {As}_{2}$ through the de Haas–van Alphen technique
journal, April 2015

One-Dimensional Edge States with Giant Spin Splitting in a Bismuth Thin Film
journal, February 2015

Dirac materials
journal, January 2014

Surface and bulk electronic structure of the strongly correlated system SmB $_{6}$ and implications for a topological Kondo insulator
journal, September 2013

Quantum spin Hall effect in a disordered hexagonal Si $_{x}$ Ge $_{1 - x}$ alloy
journal, November 2013

Quantized hall effect in superfluid helium-3 film
journal, April 1988

$d + i d^{'}$ Chiral Superconductivity in Bilayer Silicene
journal, August 2013

Floquet topological insulator in semiconductor quantum wells
journal, March 2011

Tailoring Magnetic Doping in the Topological Insulator ${Bi}_{2} {Se}_{3}$
journal, December 2012

Rocksalt SnS and SnSe: Native topological crystalline insulators
journal, December 2013

Creation of helical Dirac fermions by interfacing two gapped systems of ordinary fermions
journal, January 2013

Topological-Metal to Band-Insulator Transition in $({Bi}_{1 - x} {In}_{x})_{2} {Se}_{3}$ Thin Films
journal, October 2012

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

UPt ₃ as a Topological Crystalline Superconductor
journal, November 2013

First-principles investigations of the atomic, electronic, and thermoelectric properties of equilibrium and strained Bi $_{2}$ Se $_{3}$ and Bi $_{2}$ Te $_{3}$ including van der Waals interactions
journal, November 2012

Making Massless Dirac Fermions from a Patterned Two-Dimensional Electron Gas
journal, May 2009

Persistence of a Two-Dimensional Topological Insulator State in Wide HgTe Quantum Wells
journal, March 2015

Topological Insulator Bi2Se3 Nanowire High Performance Field-Effect Transistors
journal, April 2013

Topological insulators in the quaternary chalcogenide compounds and ternary famatinite compounds
journal, August 2011

Theoretical prediction of topological insulator in ternary rare earth chalcogenides
journal, October 2010

Stable Nontrivial $Z_{2}$ Topology in Ultrathin Bi (111) Films: A First-Principles Study
journal, September 2011

Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
journal, August 2006

Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator
journal, March 2011

The electronic properties of graphene
journal, January 2009

Topological electronic structure and Weyl semimetal in the TlBiSe $_{2}$ class of semiconductors
journal, September 2012

Topological phase transition in bulk materials described by the coherent potential approximation technique
journal, October 2012

Ambipolar Surface State Thermoelectric Power of Topological Insulator Bi ₂ Se ₃
journal, March 2014

Superconductivity near 30 K without copper: the Ba0.6K0.4BiO3 perovskite
journal, April 1988

Electronic Momentum Densities by Two-Dimensional Angular Correlation of Annihilation Radiation in Aluminum
journal, November 1976

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates
journal, August 2011

Observation of Surface Dirac Cone in High-Quality Ultrathin Epitaxial Bi ₂ Se ₃ Topological Insulator on AlN(0001) Dielectric
journal, June 2014

Weak topological insulators induced by the interlayer coupling: A first-principles study of stacked Bi $_{2}$ TeI
journal, January 2014

Positron studies of metallic YBa2Cu3O7−x
journal, January 1991

Absence of helical surface states in bulk semimetals with broken inversion symmetry
journal, March 2014

Materials science: Enter the oxides
journal, May 2009

Magnetic pyrochlore oxides
journal, January 2010

Dirac semimetals $A_{3} Bi$ $(A = Na, K, Rb)$ as $Z_{2}$ Weyl semimetals
journal, March 2015

Colloquium : Andreev reflection and Klein tunneling in graphene
journal, October 2008

Floquet chiral edge states in graphene
journal, March 2014

Topological insulators with inversion symmetry
journal, July 2007

Coherent-potential and average $t$ -matrix approximations for disordered muffin-tin alloys. II. Application to realistic systems
journal, November 1979

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

Intermediate coupling model of the cuprates
journal, May 2014

Ultrafast helicity control of surface currents in topological insulators with near-unity fidelity
journal, March 2015

Surface Scattering via Bulk Continuum States in the 3D Topological Insulator ${Bi}_{2} {Se}_{3}$
journal, July 2011

Quantum Spin Hall Effect in Graphene
journal, November 2005

Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in ${Bi}_{2} {Te}_{3}$ and ${Sb}_{2} {Te}_{3}$
journal, September 2009

Quantum Spin Hall Effect in Inverted Type-II Semiconductors
journal, June 2008

Electronic structure of the quantum spin Hall parent compound CdTe and related topological issues
journal, November 2014

Topological Oxide Insulator in Cubic Perovskite Structure
journal, April 2013

Dual-Gated Topological Insulator Thin-Film Device for Efficient Fermi-Level Tuning
journal, February 2015

Quantal Phase Factors Accompanying Adiabatic Changes
journal, March 1984

Topological edge states and electronic structures of a 2D topological insulator: Single-bilayer Bi (111)
journal, June 2013

Emergent quantum confinement at topological insulator surfaces
journal, January 2012

Vibrations in binary and ternary topological insulators: First-principles calculations and Raman spectroscopy measurements
journal, November 2012

Pressure-induced topological insulating behavior in the ternary chalcogenide Ge $_{2}$ Sb $_{2}$ Te $_{5}$
journal, August 2011

Probing the Electronic Properties of Individual MnPc Molecules Coupled to Topological States
journal, August 2014

Magnetic proximity effect at the three-dimensional topological insulator/magnetic insulator interface
journal, October 2013

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

Design Principles and Coupling Mechanisms in the 2D Quantum Well Topological Insulator $HgTe / CdTe$
journal, October 2010

Possible high-temperature superconducting state with a $d + i d$ pairing symmetry in doped graphene
journal, February 2010

Topological semimetal in a Bi-Bi $_{2}$ Se $_{3}$ infinitely adaptive superlattice phase
journal, December 2012

Temperature-Induced Coexistence of a Conducting Bilayer and the Bulk-Terminated Surface of the Topological Insulator Bi ₂ Te ₃
journal, August 2013

Engineering the quantum anomalous Hall effect in graphene with uniaxial strains
journal, December 2013

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

Coherent-potential and average $t$ -matrix approximations for disordered muffin-tin alloys. I. Formalism
journal, November 1979

Tunable topological electronic structures in Sb(111) bilayers: A first-principles study
journal, January 2013

Strain-driven onset of nontrivial topological insulating states in Zintl Sr $_{2} X$ compounds ( $X = Pb$ , Sn)
journal, October 2011

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

Fundamental Optical Absorption in $β$ -Silver Telluride
journal, February 1966

Single Crystalline Nanostructures of Topological Crystalline Insulator SnTe with Distinct Facets and Morphologies
journal, October 2013

Topological Properties Determined by Atomic Buckling in Self-Assembled Ultrathin Bi(110)
journal, December 2014

Floquet Spectrum and Transport through an Irradiated Graphene Ribbon
journal, November 2011

Ripple-modulated electronic structure of a 3D topological insulator
journal, January 2012

Evolution of Midgap States and Residual Three Dimensionality in ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$
journal, October 2005

Terahertz Response and Colossal Kerr Rotation from the Surface States of the Topological Insulator ${Bi}_{2} {Se}_{3}$
journal, February 2012

Topological metal behavior in GeBi $_{2}$ Te $_{4}$ single crystals
journal, October 2013

A first-principles studies on TlX (X=P, As)
journal, January 2008

Topological surface transport in epitaxial SnTe thin films grown on Bi $_{2}$ Te $_{3}$
journal, March 2014