Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
Open accessAbstract
We propose models of two-dimensional paramagnetic semiconductors where the intrinsic spin Hall effect is exactly quantized in integer units of a topological charge. The model describes a topological insulator in the bulk and a ``holographic metal'' at the edge, where the number of extended edge states crossing the Fermi level is dictated by (exactly equal to) the bulk topological charge. We also demonstrate the spin Hall effect explicitly in terms of the spin accumulation caused by the adiabatic flux insertion.
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Dirac points are common in two-dimensional systems.
“Dirac points are common in two-dimensional systems [46][47][48].”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [47]
Section III (pp. 3–4) develops a two-dimensional semiconductor model and mentions Dirac matrices, but does not discuss Dirac points or how common they are. A search for Dirac points and band crossings found no passage in our copy supporting that prevalence claim. (LLM, conf=0.76)
Experimental — accuracy not yet measuredIn many existing works Dirac points are observed only at time-reversal-breaking wavevectors, such as the K- and K'-points in a honeycomb lattice.
“However, in many existing works Dirac points are observed only at time-reversal-breaking wavevectors, such as the Kand K'-points in a honeycomb lattice [46][47][48].”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [47]
Section II (p. 1) mentions Haldane’s honeycomb-lattice model, but does not locate its Dirac points. Searches for “Dirac point,” “K points,” and time-reversal-related wavevectors found no passage supporting the claim that many existing works observe Dirac points only at K and K′ or other such wavevectors. (LLM, conf=0.74)
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Cites
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Flagged first, then by citations
Research works printed but not linked: 2
- 20 M. Kohmoto, Annals of Physics 160 , 355 (1985).
- 22 G. Volovik, The universe in a helium droplet (Oxford Publications, Oxford, 2003).
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<i>Colloquium</i> : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930 · see citing works
Topological insulators and superconductors
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-citationBerry phase effects on electronic properties
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Self-citationClassification of topological insulators and superconductors in three spatial dimensions
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<i>Colloquium</i> : Topological band theory
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The Quantum Anomalous Hall Effect: Theory and Experiment
Liu, C.-X., Zhang, S.-C., & Qi, X.-L. (2016) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031115-011417 · Cited by 617 · see citing works
Self-citationMassive Dirac fermions and spin physics in an ultrathin film of topological insulator
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Chiral topological superconductor from the quantum Hall state
Qi, X.-L., Hughes, T. L., & Zhang, S.-C. (2010) · Physical Review B · doi:10.1103/physrevb.82.184516 · Cited by 556 · see citing works
Self-citationQuantum anomalous Hall effect and related topological electronic states
Weng, H., Yu, R., Hu, X., Dai, X., & Fang, Z. (2015) · Advances in Physics · doi:10.1080/00018732.2015.1068524 · Cited by 506 · see citing works
Finite Size Effects on Helical Edge States in a Quantum Spin-Hall System
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Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions
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“In the second example, we propose an implementation of the Qi–Wu–Zhang (QWZ) model 47 , a well-known model of a Chern insulator on a two-dimensional square lattice, using a modification of the experimental setup in Fig.”
Cserti, J., & Dávid, G. (2010) · Physical Review B · doi:10.1103/physrevb.82.201405 · Cited by 24 · see citing works
Liu, X., Wang, Z., Xie, X. C., & Yu, Y. (2011) · Physical Review B · doi:10.1103/physrevb.83.125105 · Cited by 13 · see citing works
- Authors
- Qi, X.-L., Wu, Y.-S., & Zhang, S.-C.
- Affiliations
- Tsinghua University (CN)
- University of Utah (US)
- ORCID
- Qi, Xiao-Liang
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2006-08-10
- Volume
- 74
- Issue
- 8
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2040935135
- Cited by
- 892
- References
- 2
- Citations by year
- 2026: 48 · 2025: 86 · 2024: 82 · 2023: 75 · 2022: 64 · 2021: 63 · 2020: 99 · 2019: 44 · 2018: 48 · 2017: 37 · 2016: 46 · 2015: 35 · 2014: 28 · 2013: 34 · 2012: 20
- FWCI
- 5.16
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- arXiv (Cornell University)
- 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 › Atomic and Molecular Physics, and Optics › Magnetic properties of thin films
- Keywords
- spin Hall effect, topological quantization, topological insulators, edge states, topological charge, spin accumulation
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