Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators

Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L.

doi:10.1103/physrevb.96.245115

Title: Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators

Journal Article · Fri Dec 01 00:00:00 EST 2017 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.96.245115· OSTI ID:1540748

Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0016239

OSTI ID:: 1540748

Journal Information:: Physical Review B, Vol. 96, Issue 24; ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

References (76)

Theory of the electric polarization in crystals Resta, R. Ferroelectrics, Vol. 136, Issue 1 https://doi.org/10.1080/00150199208016065	journal	November 1992
Theory of polarization of crystalline solids King-Smith, R. D.; Vanderbilt, David Physical Review B, Vol. 47, Issue 3 https://doi.org/10.1103/PhysRevB.47.1651	journal	January 1993
Electric polarization as a bulk quantity and its relation to surface charge Vanderbilt, David; King-Smith, R. D. Physical Review B, Vol. 48, Issue 7 https://doi.org/10.1103/PhysRevB.48.4442	journal	August 1993
Towards a quantum theory of polarization in ferroelectrics: The case of ${KNbO}_{3}$ Resta, R.; Posternak, M.; Baldereschi, A. Physical Review Letters, Vol. 70, Issue 7 https://doi.org/10.1103/PhysRevLett.70.1010	journal	February 1993
Macroscopic polarization in crystalline dielectrics: the geometric phase approach Resta, Raffaele Reviews of Modern Physics, Vol. 66, Issue 3 https://doi.org/10.1103/RevModPhys.66.899	journal	July 1994
Quantal Phase Factors Accompanying Adiabatic Changes Berry, M. V. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 392, Issue 1802 https://doi.org/10.1098/rspa.1984.0023	journal	March 1984
Berry’s phase for energy bands in solids Zak, J. Physical Review Letters, Vol. 62, Issue 23 https://doi.org/10.1103/PhysRevLett.62.2747	journal	June 1989
Solitons in Polyacetylene Su, W. P.; Schrieffer, J. R.; Heeger, A. J. Physical Review Letters, Vol. 42, Issue 25 https://doi.org/10.1103/PhysRevLett.42.1698	journal	June 1979
Wannier functions in one-dimensional disordered systems: Application to fractionally charged solitons Kivelson, S. Physical Review B, Vol. 26, Issue 8 https://doi.org/10.1103/PhysRevB.26.4269	journal	October 1982
Quantization of particle transport Thouless, D. J. Physical Review B, Vol. 27, Issue 10 https://doi.org/10.1103/PhysRevB.27.6083	journal	May 1983
Quantized Hall Conductance in a Two-Dimensional Periodic Potential Thouless, D. J.; Kohmoto, M.; Nightingale, M. P. Physical Review Letters, Vol. 49, Issue 6 https://doi.org/10.1103/PhysRevLett.49.405	journal	August 1982
New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance Klitzing, K. v.; Dorda, G.; Pepper, M. Physical Review Letters, Vol. 45, Issue 6 https://doi.org/10.1103/PhysRevLett.45.494	journal	August 1980
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane, F. D. M. Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2015	journal	October 1988
Topological field theory of time-reversal invariant insulators Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng Physical Review B, Vol. 78, Issue 19, Article No. 195424 https://doi.org/10.1103/PhysRevB.78.195424	journal	November 2008
Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators Essin, Andrew M.; Moore, Joel E.; Vanderbilt, David Physical Review Letters, Vol. 102, Issue 14 https://doi.org/10.1103/PhysRevLett.102.146805	journal	April 2009
Inversion-symmetric topological insulators Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei Physical Review B, Vol. 83, Issue 24 https://doi.org/10.1103/PhysRevB.83.245132	journal	June 2011
Quantized response and topology of magnetic insulators with inversion symmetry Turner, Ari M.; Zhang, Yi; Mong, Roger S. K. Physical Review B, Vol. 85, Issue 16 https://doi.org/10.1103/PhysRevB.85.165120	journal	April 2012
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures Altland, Alexander; Zirnbauer, Martin R. Physical Review B, Vol. 55, Issue 2 https://doi.org/10.1103/PhysRevB.55.1142	journal	January 1997
Classification of topological insulators and superconductors in three spatial dimensions Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira Physical Review B, Vol. 78, Issue 19 https://doi.org/10.1103/PhysRevB.78.195125	journal	November 2008
Periodic table for topological insulators and superconductors Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings https://doi.org/10.1063/1.3149495	conference	January 2009
Surface states and topological invariants in three-dimensional topological insulators: Application to ${Bi}_{1 - x} {Sb}_{x}$ Teo, Jeffrey C. Y.; Fu, Liang; Kane, C. L. Physical Review B, Vol. 78, Issue 4, Article No. 045426 https://doi.org/10.1103/PhysRevB.78.045426	journal	July 2008
Classification of topological insulators and superconductors in the presence of reflection symmetry Chiu, Ching-Kai; Yao, Hong; Ryu, Shinsei Physical Review B, Vol. 88, Issue 7 https://doi.org/10.1103/PhysRevB.88.075142	journal	August 2013
Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to ${Sr}_{2} {RuO}_{4}$ Ueno, Yuji; Yamakage, Ai; Tanaka, Yukio Physical Review Letters, Vol. 111, Issue 8 https://doi.org/10.1103/PhysRevLett.111.087002	journal	August 2013
Topological Mirror Superconductivity Zhang, Fan; Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 111, Issue 5 https://doi.org/10.1103/PhysRevLett.111.056403	journal	August 2013
Topological mirror insulators in one dimension Lau, Alexander; van den Brink, Jeroen; Ortix, Carmine Physical Review B, Vol. 94, Issue 16 https://doi.org/10.1103/PhysRevB.94.165164	journal	October 2016
Topological insulators with inversion symmetry Fu, Liang; Kane, C. L. Physical Review B, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevB.76.045302	journal	July 2007
Entanglement and inversion symmetry in topological insulators Turner, Ari M.; Zhang, Yi; Vishwanath, Ashvin Physical Review B, Vol. 82, Issue 24 https://doi.org/10.1103/PhysRevB.82.241102	journal	December 2010
Topological Crystalline Insulators Fu, Liang Physical Review Letters, Vol. 106, Issue 10 https://doi.org/10.1103/PhysRevLett.106.106802	journal	March 2011
Bulk topological invariants in noninteracting point group symmetric insulators Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115112	journal	September 2012
Entanglement spectrum classification of $C_{n}$ -invariant noninteracting topological insulators in two dimensions Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei Physical Review B, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevB.87.035119	journal	January 2013
Existence of Majorana-Fermion Bound States on Disclinations and the Classification of Topological Crystalline Superconductors in Two Dimensions Teo, Jeffrey C. Y.; Hughes, Taylor L. Physical Review Letters, Vol. 111, Issue 4 https://doi.org/10.1103/PhysRevLett.111.047006	journal	July 2013
Classification of two-dimensional topological crystalline superconductors and Majorana bound states at disclinations Benalcazar, Wladimir A.; Teo, Jeffrey C. Y.; Hughes, Taylor L. Physical Review B, Vol. 89, Issue 22 https://doi.org/10.1103/PhysRevB.89.224503	journal	June 2014
Topological nonsymmorphic crystalline insulators Liu, Chao-Xing; Zhang, Rui-Xing; VanLeeuwen, Brian K. Physical Review B, Vol. 90, Issue 8 https://doi.org/10.1103/PhysRevB.90.085304	journal	August 2014
Topologically stable gapless phases in nonsymmorphic superconductors Kobayashi, Shingo; Yanase, Youichi; Sato, Masatoshi Physical Review B, Vol. 94, Issue 13 https://doi.org/10.1103/PhysRevB.94.134512	journal	October 2016
Topological Insulators from Group Cohomology Alexandradinata, A.; Wang, Zhijun; Bernevig, B. Andrei Physical Review X, Vol. 6, Issue 2 https://doi.org/10.1103/PhysRevX.6.021008	journal	April 2016
Antiferromagnetic topological insulators Mong, Roger S. K.; Essin, Andrew M.; Moore, Joel E. Physical Review B, Vol. 81, Issue 24 https://doi.org/10.1103/PhysRevB.81.245209	journal	June 2010
Topological classification of crystalline insulators with space group symmetry Jadaun, Priyamvada; Xiao, Di; Niu, Qian Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevB.88.085110	journal	August 2013
The space group classification of topological band-insulators Slager, Robert-Jan; Mesaros, Andrej; Juričić, Vladimir Nature Physics, Vol. 9, Issue 2 https://doi.org/10.1038/nphys2513	journal	December 2012
Topological classification with additional symmetries from Clifford algebras Morimoto, Takahiro; Furusaki, Akira Physical Review B, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevB.88.125129	journal	September 2013
Topology of crystalline insulators and superconductors Shiozaki, Ken; Sato, Masatoshi Physical Review B, Vol. 90, Issue 16 https://doi.org/10.1103/PhysRevB.90.165114	journal	October 2014
Classification of topological quantum matter with symmetries Chiu, Ching-Kai; Teo, Jeffrey C. Y.; Schnyder, Andreas P. Reviews of Modern Physics, Vol. 88, Issue 3 https://doi.org/10.1103/RevModPhys.88.035005	journal	August 2016
Classification of topological crystalline insulators based on representation theory Dong, Xiao-Yu; Liu, Chao-Xing Physical Review B, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevB.93.045429	journal	January 2016
Topological crystalline magnets: Symmetry-protected topological phases of fermions Watanabe, Haruki; Fu, Liang Physical Review B, Vol. 95, Issue 8 https://doi.org/10.1103/PhysRevB.95.081107	journal	February 2017
Topological quantum chemistry Bradlyn, Barry; Elcoro, L.; Cano, Jennifer Nature, Vol. 547, Issue 7663 https://doi.org/10.1038/nature23268	journal	July 2017
Topological crystalline materials: General formulation, module structure, and wallpaper groups Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori Physical Review B, Vol. 95, Issue 23 https://doi.org/10.1103/PhysRevB.95.235425	journal	June 2017
Quantized electric multipole insulators Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L. Science, Vol. 357, Issue 6346 https://doi.org/10.1126/science.aah6442	journal	July 2017
Equivalent expression of $Z_{2}$ topological invariant for band insulators using the non-Abelian Berry connection Yu, Rui; Qi, Xiao Liang; Bernevig, Andrei Physical Review B, Vol. 84, Issue 7 https://doi.org/10.1103/PhysRevB.84.075119	journal	August 2011
Model Characterization of Gapless Edge Modes of Topological Insulators Using Intermediate Brillouin-Zone Functions Fidkowski, Lukasz; Jackson, T. S.; Klich, Israel Physical Review Letters, Vol. 107, Issue 3 https://doi.org/10.1103/PhysRevLett.107.036601	journal	July 2011
Wilson-loop characterization of inversion-symmetric topological insulators Alexandradinata, A.; Dai, Xi; Bernevig, B. Andrei Physical Review B, Vol. 89, Issue 15 https://doi.org/10.1103/PhysRevB.89.155114	journal	April 2014
Adiabatic Pumping of Chern-Simons Axion Coupling Taherinejad, Maryam; Vanderbilt, David Physical Review Letters, Vol. 114, Issue 9 https://doi.org/10.1103/PhysRevLett.114.096401	journal	March 2015
Surface theorem for the Chern-Simons axion coupling Olsen, Thomas; Taherinejad, Maryam; Vanderbilt, David Physical Review B, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevB.95.075137	journal	February 2017
Surface polarization and edge charges Zhou, Yuanjun; Rabe, Karin M.; Vanderbilt, David Physical Review B, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevB.92.041102	journal	July 2015
Quantum-Mechanical Position Operator in Extended Systems Resta, Raffaele Physical Review Letters, Vol. 80, Issue 9 https://doi.org/10.1103/PhysRevLett.80.1800	journal	March 1998
Dynamics of Band Electrons in Electric and Magnetic Fields Wannier, Gregory H. Reviews of Modern Physics, Vol. 34, Issue 4 https://doi.org/10.1103/RevModPhys.34.645	journal	October 1962
Maximally localized generalized Wannier functions for composite energy bands Marzari, Nicola; Vanderbilt, David Physical Review B, Vol. 56, Issue 20 https://doi.org/10.1103/PhysRevB.56.12847	journal	November 1997
Maximally localized Wannier functions for entangled energy bands Souza, Ivo; Marzari, Nicola; Vanderbilt, David Physical Review B, Vol. 65, Issue 3 https://doi.org/10.1103/PhysRevB.65.035109	journal	December 2001
Elementary Excitations of a Linearly Conjugated Diatomic Polymer Rice, M. J.; Mele, E. J. Physical Review Letters, Vol. 49, Issue 19 https://doi.org/10.1103/PhysRevLett.49.1455	journal	November 1982
Direct measurement of the Zak phase in topological Bloch bands Atala, Marcos; Aidelsburger, Monika; Barreiro, Julio T. Nature Physics, Vol. 9, Issue 12 https://doi.org/10.1038/nphys2790	journal	November 2013
Topological Charge Pumping in a One-Dimensional Optical Lattice Wang, Lei; Troyer, Matthias; Dai, Xi Physical Review Letters, Vol. 111, Issue 2 https://doi.org/10.1103/PhysRevLett.111.026802	journal	July 2013
Geometrical Pumping with a Bose-Einstein Condensate Lu, H. -I; Schemmer, M.; Aycock, L. M. Physical Review Letters, Vol. 116, Issue 20 https://doi.org/10.1103/PhysRevLett.116.200402	journal	May 2016
Electric Polarization in a Chern Insulator Coh, Sinisa; Vanderbilt, David Physical Review Letters, Vol. 102, Issue 10 https://doi.org/10.1103/PhysRevLett.102.107603	journal	March 2009
Topological indices, defects, and Majorana fermions in chiral superconductors Asahi, Daichi; Nagaosa, Naoto Physical Review B, Vol. 86, Issue 10 https://doi.org/10.1103/PhysRevB.86.100504	journal	September 2012
Majorana zero modes in dislocations of ${Sr}_{2} {RuO}_{4}$ Hughes, Taylor L.; Yao, Hong; Qi, Xiao-Liang Physical Review B, Vol. 90, Issue 23 https://doi.org/10.1103/PhysRevB.90.235123	journal	December 2014
Electron localization in the insulating state: Application to crystalline semiconductors Sgiarovello, Claudia; Peressi, Maria; Resta, Raffaele Physical Review B, Vol. 64, Issue 11 https://doi.org/10.1103/PhysRevB.64.115202	journal	August 2001
Wannier center sheets in topological insulators Taherinejad, Maryam; Garrity, Kevin F.; Vanderbilt, David Physical Review B, Vol. 89, Issue 11 https://doi.org/10.1103/PhysRevB.89.115102	journal	March 2014
Smooth gauge and Wannier functions for topological band structures in arbitrary dimensions Winkler, Georg W.; Soluyanov, Alexey A.; Troyer, Matthias Physical Review B, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevB.93.035453	journal	January 2016
Manifestly gauge-independent formulations of the $Z_{2}$ invariants Prodan, Emil Physical Review B, Vol. 83, Issue 23 https://doi.org/10.1103/PhysRevB.83.235115	journal	June 2011
Smooth gauge for topological insulators Soluyanov, Alexey A.; Vanderbilt, David Physical Review B, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevB.85.115415	journal	March 2012
Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect Vishwanath, Ashvin; Senthil, T. Physical Review X, Vol. 3, Issue 1 https://doi.org/10.1103/PhysRevX.3.011016	journal	February 2013
A time-reversal invariant topological phase at the surface of a 3D topological insulator Bonderson, Parsa; Nayak, Chetan; Qi, Xiao-Liang Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 09 https://doi.org/10.1088/1742-5468/2013/09/P09016	journal	September 2013
Gapped symmetry preserving surface state for the electron topological insulator Wang, Chong; Potter, Andrew C.; Senthil, T. Physical Review B, Vol. 88, Issue 11 https://doi.org/10.1103/PhysRevB.88.115137	journal	September 2013
Symmetry enforced non-Abelian topological order at the surface of a topological insulator Chen, Xie; Fidkowski, Lukasz; Vishwanath, Ashvin Physical Review B, Vol. 89, Issue 16 https://doi.org/10.1103/PhysRevB.89.165132	journal	April 2014
Symmetry-respecting topologically ordered surface phase of three-dimensional electron topological insulators Metlitski, Max A.; Kane, C. L.; Fisher, Matthew P. A. Physical Review B, Vol. 92, Issue 12 https://doi.org/10.1103/PhysRevB.92.125111	journal	September 2015
$(d - 2)$ -Dimensional Edge States of Rotation Symmetry Protected Topological States Song, Zhida; Fang, Zhong; Fang, Chen Physical Review Letters, Vol. 119, Issue 24 https://doi.org/10.1103/PhysRevLett.119.246402	journal	December 2017
Reflection-Symmetric Second-Order Topological Insulators and Superconductors Langbehn, Josias; Peng, Yang; Trifunovic, Luka Physical Review Letters, Vol. 119, Issue 24 https://doi.org/10.1103/PhysRevLett.119.246401	journal	December 2017
Boundary Green functions of topological insulators and superconductors Peng, Yang; Bao, Yimu; von Oppen, Felix Physical Review B, Vol. 95, Issue 23 https://doi.org/10.1103/PhysRevB.95.235143	journal	June 2017

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