Simplified topological invariants for interacting insulators

Physical Review X

Volumn 2, Issue 3, 2012, Pages

  Wang, Zhong ^a   Zhang, Shou Cheng ^b  

^a TSINGHUA UNIVERSITY   (China)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL ALGORITHMS; INTERACTING SYSTEM; TOPOLOGICAL INSULATORS; TOPOLOGICAL INVARIANTS; TOPOLOGICAL ORDER; TWO-DIMENSION; UNIFIED DESCRIPTION; ZERO FREQUENCY;

GREEN'S FUNCTION;

TOPOLOGY;

EID: 84867472230     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.2.031008     Document Type: Article

References (37)

1. X. L. Qi and S. C. Zhang, The Quantum Spin Hall Effect and Topological Insulators, Phys. Today 63, 33 (2010).
2. J. Moore, The Birth of Topological Insulators, Nature (London) 464, 194 (2010).
3. M. Z. Hasan and C. L. Kane, Colloquium: Topological Insulators, Rev. Mod. Phys. 82, 3045 (2010).
4. Xiao-Liang Qi and Shou-Cheng Zhang, Topological Insulators and Superconductors, Rev. Mod. Phys. 83, 1057 (2011).
5. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405 (1982).
6. C. L. Kane and E. J. Mele, Z2 Topological Order and the Quantum Spin Hall Effect, Phys. Rev. Lett. 95, 146802 (2005).
7. J. E. Moore and L. Balents, Topological Invariants of Time-Reversal-Invariant Band Structures, Phys. Rev. B 75, 121306 (2007).
8. R. Roy, Topological Phases and the Quantum Spin Hall Effect in Three Dimensions, Phys. Rev. B 79, 195322 (2009).
9. Xiao-Liang Qi, Taylor Hughes, and Shou-Cheng Zhang, Topological Field Theory of Time-Reversal Invariant Insulators, Phys. Rev. B 78, 195424 (2008).
10. S. Raghu, Xiao-Liang Qi, C. Honerkamp, and Shou-Cheng Zhang, Topological Mott Insulators, Phys. Rev. Lett. 100, 156401 (2008).
11. 3,"Phys. Rev. Lett. 102, 256403 (2009).
12. Yi Zhang, Ying Ran, and Ashvin Vishwanath, Topological Insulators in Three Dimensions from Spontaneous Symmetry Breaking, Phys. Rev. B 79, 245331 (2009).
13. B. Seradjeh, J. E. Moore, and M. Franz, Exciton Condensation and Charge Fractionalization in a Topological Insulator Film, Phys. Rev. Lett. 103, 066402 (2009).
14. D. A. Pesin and Leon Balents, Mott Physics and Band Topology in Materials with Strong Spin-Orbit Interaction, Nature Phys. 6, 376 (2010).
15. L. Fidkowski and A. Kitaev, Effects of Interactions on the Topological Classificaiton of Free Fermion Systems, Phys. Rev. B 81, 134509 (2010).
16. Rundong Li, Jing Wang, Xiao-Liang Qi, and Shou-Cheng Zhang, Dynamical Axion Field in Topological Magnetic Insulators, Nature Phys. 6, 284 (2010).
17. Maxim Dzero, Kai Sun, Victor Galitski, and Piers Coleman, Topological Kondo Insulators, Phys. Rev. Lett. 104, 106408 (2010).
18. Stephan Rachel and Karyn Le Hur, Topological Insulators and Spin-Charge Separation from Mott Physics, arXiv:1003.2238.
19. Xiao Zhang, Haijun Zhang, Claudia Felser, and Shou-Cheng Zhang, Actinide Topological Insulator Materials with Strong Interaction, arXiv:1111.1267.
20. Titus Neupert, Luiz Santos, Shinsei Ryu, Claudio Chamon, and Christopher Mudry, Topological Hubbard Model and Its High-Temperature Quantum Hall Effect, Phys. Rev. Lett. 108, 046806 (2012).
21. R. B. Laughlin, Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Phys. Rev. Lett. 50, 1395 (1983).
22. Zhong Wang, Xiao-Liang Qi, and Shou-Cheng Zhang, Topological Order Parameters for Interacting Topological Insulators, Phys. Rev. Lett. 105, 256803 (2010).
23. Lei Wang, Xi Dai, and X. C. Xie, Frequency Domain Winding Number and Interaction Effect on Topological Insulators, Phys. Rev. B 84, 205116 (2011).
24. Lei Wang, Hua Jiang, Xi Dai, and X. C. Xie, Pole Expansion of Self-Energy and Interaction Effect on Topological Insulators, arXiv:1109.6292.
25. V. Gurarie, Single-Particle Green's Functions and Interacting Topological Insulators, Phys. Rev. B 83, 085426 (2011).
26. Kuang-Ting Chen and Patrick A. Lee, Unified Formalism for Calculating Polarization, Magnetization, and More in a Periodic Insulator, Phys. Rev. B 84, 205137 (2011).
27. Zhong Wang, Xiao-Liang Qi, and Shou-Cheng Zhang, Topological Invariants for Interacting Topological Insulators with Inversion Symmetry, Phys. Rev. B 85, 165126 (2012).
28. X. L. Qi, Y. S. Wu, and S. C. Zhang, Topological Quantization of the Spin Hall Effect in Two-Dimensional Paramagnetic Semiconductors, Phys. Rev. B 74, 085308 (2006).
29. 1_yMnyTe Quantum Wells, Phys. Rev. Lett. 101, 146802 (2008).
30. Rui Yu, Wei Zhang, Hai-Jun Zhang, Shou-Cheng Zhang, Xi Dai, and Zhong Fang, Quantized Anomalous Hall Effect in Magnetic Topological Insulators, Science 329, 61 (2010)
31. Qian Niu, D. J. Thouless, and Yong-Shi Wu, Quantized Hall Conductance as a Topological Invariant, Phys. Rev. B 31, 3372 (1985).
32. K. Ishikawa and T. Matsuyama, Magnetic Field Induced Multicomponent QED3 and Quantum Hall Effect, Z. Phys. C 33, 41 (1986).
33. G. E. Volovik, The Universe in a Helium Droplet (Oxford University Press, New York, 2003).
34. S. C. Zhang and J. P. Hu, A Four-Dimensional Generalization of the Quantum Hall Effect, Science 294, 823 (2001).
35. Ara Go, William Witczak-Krempa, Gun Sang Jeon, Kwon Park, and Yong Baek Kim, Correlated Topological Phases in 3D Complex Oxides via Green's Functions, arXiv:1202.4460.
36. Zhong Wang, Xiao-Liang Qi, and Shou-Cheng Zhang, Equivalent Topological Invariants of Topological Insulators, New J. Phys. 12, 065007 (2010).
37. Liang Fu and C. L. Kane, Time Reversal Polarization and a Z2 Adiabatic Spin Pump, Phys. Rev. B 74, 195312 (2006).