Quantum Spin Hall Effect in Graphene
Open accessAbstract
We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are nonchiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.
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The QSHE is a topological insulator characterized by a Z2 topological invariant, taking values 0 and 1 in the trivial and QSH phase, respectively.
“The QSHE is a topological insulator (TI) characterized by a Z 2 topological invariant [45], taking up values 0 and 1 in the trivial and the QSH phase, respectively.”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [45]
The paper (pp. 1–2) describes the QSH state in graphene as topologically distinct from an ordinary insulator, supporting the distinction between QSH and trivial phases. It does not state that the phases are characterized by a Z2 invariant or assign them the values 0 and 1. (LLM, conf=0.88)
Experimental — accuracy not yet measuredIn 2005, a topologically nontrivial 2D QSHE system was proposed by Kane and Mele.
“In 2005, a topologically nontrivial 2D QSHE system was proposed by Kane and Mele [44,45].”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [45]
In 2005, a topologically nontrivial 2D QSHE system was proposed by Kane and Mele.
“In 2005, a topologically nontrivial 2D QSHE system was proposed by Kane and Mele [44,45].”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [44]
The Kane-Mele QSHE system is a spin-1/2 system on a honeycomb lattice with a spin-orbit interaction.
“It is a spin1 / 2 system on a honeycomb lattice with a spin-orbit interaction.”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [44]
The Kane-Mele QSHE system is a spin-1/2 system on a honeycomb lattice with a spin-orbit interaction.
“It is a spin1 / 2 system on a honeycomb lattice with a spin-orbit interaction.”
From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [45]
In graphene the degeneracy is removed by spin-orbit coupling and its gapped phase is the prototype quantum spin Hall insulator (Kane and Mele, 2005).
“In graphene this degeneracy is removed by spin-orbit coupling and its gapped phase is the prototype quantum spin Hall insulator (Kane and Mele, 2005).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Kane and Mele, 2005
The planar Hall effect in ferromagnets arises from resistivity anisotropy caused by anisotropic magnetization.
“The PHE, a well-known phenomenon observed in ferromagnets, is due to the resistivity anisotropy caused by anisotropic magnetization (316).”
From Transport of Topological Semimetals (2019) · cites this paper as [316]
The paper discusses the quantum spin Hall effect in graphene (p. 1) and spin-filtered edge transport (p. 3). Searches for the planar Hall effect and anisotropic magnetoresistance found no passage addressing resistivity anisotropy caused by magnetization in ferromagnets. (LLM, conf=0.76)
Experimental — accuracy not yet measuredA hexagonal lattice of epsilon/mu-matched rods implies Dirac-cone linear photonic dispersion near the K and K' corner points of the Brillouin zone.
“The hexagonal symmetry of the structure implies Dirac-cone linear photonic dispersion near the K and K corner points of the Brillouin zone [ 16] (see inset to Fig. 1a) that simplifies mapping to electronic systems [ 1, 2].”
From Photonic topological insulators (2013) · cites this paper as [2]
The effective low-energy Hamiltonian for the photonic meta-crystal is identical to the Hamiltonian introduced in Ref. [2] for graphene with spin-orbit coupling.
“The new Hamiltonian ℋ acts on the wavefunctions = [ , ] where = [ ( ) + ( ), ( ) + ( ), ( ) ( ), ( ) ( )] and is identical to that introduced in Ref. [ 2] for graphene with spin-orbit coupling.”
From Photonic topological insulators (2013) · cites this paper as [2]
Electromagnetic wave propagation in the proposed system reflects a quantized photonic spin Hall effect exactly analogous to the quantum spin Hall effect in electronic systems.
“Electromagnetic wave propagation therefore reflects a quantized photonic spin Hall effect that is exactly analogous to the quantum spin Hall effect in electronic systems [ 2, 41].”
From Photonic topological insulators (2013) · cites this paper as [2]
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“In graphene this degeneracy is removed by spin-orbit coupling and its gapped phase is the prototype quantum spin Hall insulator (Kane and Mele, 2005).”
BackgroundInfluentialSelf-citation
- Authors
- Kane, C. L., & Mele, E. J.
- Affiliations
- University of Pennsylvania (US)
- ORCID
- Kane, C. L.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-11-23
- Volume
- 95
- Issue
- 22
- Pages
- 226801-226801
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2030164271
- Cited by
- 8,197
- References
- 3
- Citations by year
- 2026: 292 · 2025: 494 · 2024: 550 · 2023: 502 · 2022: 545 · 2021: 568 · 2020: 709 · 2019: 557 · 2018: 551 · 2017: 502 · 2016: 531 · 2015: 464 · 2014: 422 · 2013: 400 · 2012: 349
- FWCI
- 34.25
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (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 › Materials Science › Materials Chemistry › Graphene research and applications
- Keywords
- quantum spin Hall effect, graphene, spin-orbit coupling, edge states, spin Hall conductance, charge conductance, Rashba spin-orbit coupling, topological insulators, low-temperature electronic structure, chemical potential dependence, temperature dependence
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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