The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
Computing topological invariants without inversion symmetry
Open accessAbstract
We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal ($\mathcal{T}$) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one dimension. Although this gauge is not smoothly defined on the two torus, it respects the $\mathcal{T}$ symmetry of the system and allows for a definition of the ${\mathbb{Z}}_{2}$ invariant in terms of time-reversal polarization. In 3D we apply the 2D approach to $\mathcal{T}$-invariant planes. We illustrate the method with first-principles calculations on GeTe and on HgTe under $[001]$ and $[111]$ strain. Our approach differs from ones used previously for noncentrosymmetric materials and should be easier to implement in ab initio code packages.
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Cites
Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
Bernevig, B. A., Hughes, T. L., & Zhang, S.-C. (2006) · Science · doi:10.1126/science.1133734 · Cited by 7,090
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.405 · Cited by 6,973
Z 2 Topological Order and the Quantum Spin Hall Effect
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.146802 · Cited by 6,460
Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface
Zhang, H., Liu, C.-X., Qi, X.-L., Dai, X., Fang, Z., & Zhang, S.-C. (2009) · Nature Physics · doi:10.1038/nphys1270 · Cited by 6,359
Quantum Spin Hall Insulator State in HgTe Quantum Wells
König, M., Wiedmann, S., Brüne, C., Roth, A., Buhmann, H., Molenkamp, L. W., Qi, X.-L., & Zhang, S.-C. (2007) · Science · doi:10.1126/science.1148047 · Cited by 6,151
Topological Insulators in Three Dimensions
Fu, L., Kane, C. L., & Mele, E. J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.106803 · Cited by 4,651
Topological insulators with inversion symmetry
Fu, L., & Kane, C. L. (2007) · Physical Review B · doi:10.1103/physrevb.76.045302 · Cited by 4,252
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y. S., Cava, R. J., et al. (2009) · Nature Physics · doi:10.1038/nphys1274 · Cited by 3,765
Experimental Realization of a Three-Dimensional Topological Insulator, Bi 2 Te 3
Chen, Y. L., Analytis, J. G., Chu, J.-H., Liu, Z. K., Mo, S.-K., Qi, X. L., Zhang, H. J., Lu, D. H., Dai, X., Fang, Z., et al. (2009) · Science · doi:10.1126/science.1173034 · Cited by 3,585
A topological Dirac insulator in a quantum spin Hall phase
Hsieh, D., Qian, D., Wray, L., Xia, Y., Hor, Y. S., Cava, R. J., & Hasan, M. Z. (2008) · Nature · doi:10.1038/nature06843 · Cited by 3,523
Berry’s phase for energy bands in solids
Zak, J. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.2747 · Cited by 1,950
The quantum spin Hall effect and topological insulators
Qi, X.-L., & Zhang, S.-C. (2010) · Physics Today · doi:10.1063/1.3293411 · Cited by 1,283
Observation of Unconventional Quantum Spin Textures in Topological Insulators
Hsieh, D., Xia, Y., Wray, L., Qian, D., Pal, A., Dil, J. H., Osterwalder, J., Meier, F., Bihlmayer, G., Kane, C. L., et al. (2009) · Science · doi:10.1126/science.1167733 · Cited by 1,239
Tunable multifunctional topological insulators in ternary Heusler compounds
Chadov, S., Qi, X., Kübler, J., Fecher, G. H., Felser, C., & Zhang, S. C. (2010) · Nature Materials · doi:10.1038/nmat2770 · Cited by 927
Z2classification of quantum spin Hall systems: An approach using time-reversal invariance
Roy, R. (2009) · Physical Review B · doi:10.1103/physrevb.79.195321 · Cited by 299
Cited by
Maximally localized Wannier functions: Theory and applications
Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I., & Vanderbilt, D. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1419 · Cited by 3,283
Self-citationWannierTools: An open-source software package for novel topological materials
Wu, Q., Zhang, S., Song, H.-F., Troyer, M., & Soluyanov, A. A. (2018) · Computer Physics Communications · doi:10.1016/j.cpc.2017.09.033 · Cited by 2,724
Self-citationSoluyanov, A. A., Gresch, D., Wang, Z., Wu, Q., Troyer, M., Dai, X., & Bernevig, B. A. (2015) · Nature · doi:10.1038/nature15768 · Cited by 2,526
Self-citationMounet, N., Gibertini, M., Schwaller, P., Campi, D., Merkys, A., Marrazzo, A., Sohier, T., Castelli, I. E., Cepellotti, A., Pizzi, G., et al. (2018) · Nature Nanotechnology · doi:10.1038/s41565-017-0035-5 · Cited by 1,863
Wang, L., Shi, Y., Liu, M., Zhang, A., Hong, Y.-L., Li, R., Gao, Q., Chen, M., Ren, W., Cheng, H.-M., et al. (2021) · Nature Communications · doi:10.1038/s41467-021-22324-8 · Cited by 466
Metadata
- Authors
- Soluyanov, A. A., & Vanderbilt, D.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2011-06-02
- Volume
- 83
- Issue
- 23
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1985457852
- Cited by
- 574
- References
- 16
- FWCI
- 4.34
- Type
- journal article
- Language
- en
- Open access
- green
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