The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
General theorem relating the bulk topological number to edge states in two-dimensional insulators
Open accessAbstract
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two-dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a nonvanishing Chern number, even if it is defined for a nonconserved quantity such as spin in the case of the spin Hall effect, one can always infer the existence of gapless edge states under certain twisted boundary conditions that allow tunneling between edges. This relation is robust against disorder and interactions, and it provides a unified topological classification of both the quantum (charge) Hall effect and the quantum spin Hall effect. In addition, it reconciles the apparent conflict between the stability of bulk topological order and the instability of gapless edge states in systems with open boundaries (a known happening in the spin Hall case). The consequences of time reversal invariance for bulk topological order and edge state dynamics are further studied in the present framework.
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Citations
Cites
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
The Universe in a Helium Droplet
Volovik, G. E. (2009) · doi:10.1093/acprof:oso/9780199564842.001.0001 · Cited by 2,632
Halperin, B. I. (1982) · Physical Review B · doi:10.1103/physrevb.25.2185 · Cited by 2,547
Chern number and edge states in the integer quantum Hall effect
Hatsugai, Y. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.3697 · Cited by 1,499
Helical Liquid and the Edge of Quantum Spin Hall Systems
Wu, C., Bernevig, B. A., & Zhang, S.-C. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.106401 · Cited by 759
Self-citationStability of the quantum spin Hall effect: Effects of interactions, disorder, andZ2topology
Xu, C., & Moore, J. E. (2006) · Physical Review B · doi:10.1103/physrevb.73.045322 · Cited by 571
A Four-Dimensional Generalization of the Quantum Hall Effect
Zhang, S.-C., & Hu, J. (2001) · Science · doi:10.1126/science.294.5543.823 · Cited by 530
Self-citation
Cited by
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
Self-citationOzawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
Lu, L., Joannopoulos, J. D., & Soljačić, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.248 · Cited by 3,655
Topological field theory of time-reversal invariant insulators
Qi, X.-L., Hughes, T. L., & Zhang, S.-C. (2008) · Physical Review B · doi:10.1103/physrevb.78.195424 · Cited by 3,329
Self-citationTopological invariants of time-reversal-invariant band structures
Moore, J. E., & Balents, L. (2007) · Physical Review B · doi:10.1103/physrevb.75.121306 · Cited by 2,350
Metadata
- Authors
- Qi, X.-L., Wu, Y.-S., & Zhang, S.-C.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2006-07-26
- Volume
- 74
- Issue
- 4
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2273782342
- Cited by
- 262
- References
- 8
- FWCI
- 2.36
- Type
- journal article
- Language
- en
- Open access
- green
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