Helical Liquid and the Edge of Quantum Spin Hall Systems
Open accessAbstract
The edge states of the recently proposed quantum spin Hall systems constitute a new symmetry class of one-dimensional liquids dubbed the "helical liquid," where the spin orientation is determined by the direction of electron motion. We prove a no-go theorem which states that a helical liquid with an odd number of components cannot be constructed in a purely 1D lattice system. In a helical liquid with an odd number of components, a uniform gap in the ground state can appear when the time-reversal symmetry is spontaneously broken by interactions. On the other hand, a correlated two-particle backscattering term by an impurity can become relevant while keeping the time-reversal invariance.
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If there are two Kramers pairs of edge modes, a right-mover can back-scatter to the left-mover that is not its time-reversal conjugate, and this process will in general eliminate these two Kramers pairs from the low-energy theory.
“However, if we have two Kramers pairs of edge modes, then a right-mover can back-scatter to the left-mover that is not its time-reversal conjugate (62,63). This process will, in general, eliminate these two Kramers pairs from the low-energy theory.”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [63]
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Cites
Spintronics: A Spin-Based Electronics Vision for the Future
Wolf, S. A., Awschalom, D. D., Buhrman, R. A., Daughton, J. M., von Molnár, S., Roukes, M. L., Chtchelkanova, A., & Treger, D. M. (2001) · Science · doi:10.1126/science.1065389 · Cited by 11,464 · see citing works
Quantum Spin Hall Effect in Graphene
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.226801 · Cited by 8,197 · see citing works
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.146802 · Cited by 6,460 · see citing works
Haldane, F. D. M. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2015 · Cited by 6,301 · see citing works
Universal Intrinsic Spin Hall Effect
Sinova, J., Culcer, D., Niu, Q., Sinitsyn, N. A., Jungwirth, T., & MacDonald, A. H. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.126603 · Cited by 2,156 · see citing works
Dissipationless Quantum Spin Current at Room Temperature
Murakami, S., Nagaosa, N., & Zhang, S. (2003) · Science · doi:10.1126/science.1087128 · Cited by 1,947 · see citing works
Self-citationAbsence of neutrinos on a lattice
Nielsen, H. B., & Ninomiya, M. (1981) · Nuclear Physics B · doi:10.1016/0550-3213(81)90361-8 · Cited by 1,719 · see citing works
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 · see citing works
Wunderlich, J., Kaestner, B., Sinova, J., & Jungwirth, T. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.047204 · Cited by 1,494 · see citing works
Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas
Kane, C. L., & Fisher, M. P. A. (1992) · Physical review. B, Condensed matter · doi:10.1103/physrevb.46.15233 · Cited by 1,114 · see citing works
Nozières, P., & Blandin, A. (1980) · Journal de physique · doi:10.1051/jphys:01980004103019300 · Cited by 1,003 · see citing works
Absence of neutrinos on a lattice
Nielsen, H. B., & Ninomiya, M. (1981) · Nuclear Physics B · doi:10.1016/0550-3213(81)90524-1 · Cited by 964 · see citing works
Anderson localization and interactions in one-dimensional metals
Giamarchi, T., & Schulz, H. J. (1988) · Physical review. B, Condensed matter · doi:10.1103/physrevb.37.325 · Cited by 859 · see citing works
Anderson, P. W., Yuval, G., & Hamann, D. R. (1970) · Physical review. B, Solid state · doi:10.1103/physrevb.1.4464 · Cited by 575 · see citing works
Xu, C., & Moore, J. E. (2006) · Physical Review B · doi:10.1103/physrevb.73.045322 · Cited by 571 · see citing works
Current-Induced Spin Polarization in Strained Semiconductors
Kato, Y. K., Myers, R. C., Gossard, A. C., et al. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.176601 · Cited by 442 · see citing works
Suppression of the persistent spin Hall current by defect scattering
Inoue, J.-I., Bauer, G. E. W., & Molenkamp, L. W. (2004) · Physical Review B · doi:10.1103/physrevb.70.041303 · Cited by 422 · see citing works
Murakami, S., Nagaosa, N., & Zhang, S.-C. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.156804 · Cited by 346 · see citing works
Self-citationNondissipative Spin Hall Effect via Quantized Edge Transport
Sheng, L., Sheng, D. N., Ting, C. S., et al. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.136602 · Cited by 219 · see citing works
Intrinsic Spin Hall Effect in the Two-Dimensional Hole Gas
Bernevig, B. A., & Zhang, S.-C. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.016801 · Cited by 162 · see citing works
Self-citationAbsence of vertex correction for the spin Hall effect in p -type semiconductors
Murakami, S. (2004) · Physical Review B · doi:10.1103/physrevb.69.241202 · Cited by 137 · see citing works
Competing Effects of Interactions and Spin-Orbit Coupling in a Quantum Wire
Gritsev, V., Japaridze, G. I., Pletyukhov, M., et al. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.137207 · Cited by 59 · see citing works
Spin Current and Accumulation Generated by the Spin Hall Insulator
Onoda, M., & Nagaosa, N. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.106601 · Cited by 47 · see citing works
Spin-orbit scattering and the Kondo effect
Meir, Y., & Wingreen, N. S. (1994) · Physical review. B, Condensed matter · doi:10.1103/physrevb.50.4947 · Cited by 39 · see citing works
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Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930 · see citing works
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Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394 · see citing works
Self-citationQuantum 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 · see citing works
Self-citationQuantum 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 · see citing works
Self-citationTopological insulators with inversion symmetry
Fu, L., & Kane, C. L. (2007) · Physical Review B · doi:10.1103/physrevb.76.045302 · Cited by 4,252 · see citing works
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Schnyder, A. P., Ryu, S., Furusaki, A., & Ludwig, A. W. W. (2008) · Physical Review B · doi:10.1103/physrevb.78.195125 · Cited by 3,322 · see citing works
Topological 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 · see citing works
Murakami, S. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/9/356 · Cited by 1,176 · see citing works
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 · see citing works
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Roth, A., Brüne, C., Buhmann, H., Molenkamp, L. W., Maciejko, J., Qi, X.-L., & Zhang, S.-C. (2009) · Science · doi:10.1126/science.1174736 · Cited by 916 · see citing works
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Finite Size Effects on Helical Edge States in a Quantum Spin-Hall System
Zhou, B., Lu, H.-Z., Chu, R.-L., Shen, S.-Q., & Niu, Q. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.246807 · Cited by 494 · see citing works
Roy, R. (2009) · Physical Review B · doi:10.1103/physrevb.79.195321 · Cited by 299 · see citing works
Single valley Dirac fermions in zero-gap HgTe quantum wells
Büttner, B., Liu, C. X., Tkachov, G., Novik, E. G., Brüne, C., Buhmann, H., Hankiewicz, E. M., Recher, P., Trauzettel, B., Zhang, S. C., et al. (2011) · Nature Physics · doi:10.1038/nphys1914 · Cited by 284 · see citing works
Self-citation
- Authors
- Wu, C., Bernevig, B. A., & Zhang, S.-C.
- Affiliations
- University of California, Santa Barbara (US)
- Stanford University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-03-14
- Volume
- 96
- Issue
- 10
- Pages
- 106401-106401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1993499159
- Cited by
- 759
- References
- 24
- Citations by year
- 2026: 16 · 2025: 26 · 2024: 29 · 2023: 22 · 2022: 27 · 2021: 36 · 2020: 37 · 2019: 36 · 2018: 40 · 2017: 49 · 2016: 48 · 2015: 54 · 2014: 56 · 2013: 67 · 2012: 66
- FWCI
- 13.12
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- quantum spin Hall effect, edge states, no-go theorem, time-reversal symmetry breaking, spontaneous symmetry breaking, backscattering, impurity scattering, interacting electrons, topological phases
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