Quantum Spin Hall Effect in Graphene
2005 · paper · Physics
A theoretical study of spin-orbit interactions in a single plane of graphene. It finds that, at low temperature, graphene becomes a quantum spin Hall insulator: insulating in the bulk, with spin-carrying edge states that resist disorder.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
3 findings
Reference or label Wrong equation pointer in the body text: "The edge states can be seen by solving (7) in a strip geometry"; the tight-binding model is Eq. (6), while Eq. (7) is the microscopic V_SO on page 4.
- p. 2 right column, paragraph after Eq. (6)
The edge states can be seen by solving (7) in a strip ge-
- p. 2 Eq. (6) and following text
At low energy (6) reduces to (2,3)
- p. 2 edge states paragraph
solving (7) in a strip ge-
- p. 3 Fig. 1 caption
modeled by (7) with t2/t
Judge's note: Page 2 image: the tight-binding Hamiltonian is numbered (6), the sentence just before says "At low energy (6) reduces to (2,3)", and the next sentence says "solving (7)". Page 4 image: Eq. (7) is V_SO = ħ/(4m²c²) s·(∇V×p), which is not a lattice model. This verdict covers the body-text pointer only; the Fig. 1 caption instance is judged under C010 and the "(8)" instance under C013.
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Reference or label Fig. 1 caption has a wrong equation pointer: "modeled by (7) with t2/t = .03"; the tight-binding model containing t and t2 is Eq. (6).
- p. 3 Fig. 1 caption
modeled by (7) with t2/t = .03
Judge's note: Page 3 image: the caption reads "modeled by (7) with t2/t = .03". Page 2 image: Eq. (6) is the second-neighbour tight-binding model with t and t2. Page 4 image: Eq. (7) is V_SO, which contains neither. Same off-by-one shift as C004, but a separate location (figure caption), so it is kept as its own item.
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Reference or label Wrong equation pointer: "We thus evaluate the expectation value of (8) in the basis of states given in (1)"; the SO interaction being evaluated is Eq. (7), while Eq. (8) is the RG flow equations.
- p. 4 left column, after Eq. (7)
evaluate the expectation value of (8) in the basis of states
- p. 4 SO estimate paragraph
We thus evaluate the expectation value of (8) in the basis
- p. 4 SO estimate paragraph
expectation value of (8) in the basis of states
- p. 4 paragraph after Eq. (7)
evaluate the expectation value of (8)
Judge's note: Page 4 image: Eq. (7) is V_SO, printed immediately above the sentence. Eq. (8) is dg/dℓ = −g²/4; dΔso/dℓ = gΔso/2, which is not an operator with an expectation value. Evident fix: (7).
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14 minor (typos and the like; most checked by the judge only)
Reference or label Citation query: "For Ez ∼50V/300nm[3] this gives λR ∼.5mK" cites Ref. [3] (Y.K. Kato et al., Science 306, 1910), which the paper itself uses for the spin Hall effect in GaAs; the gated graphene films are Ref. [6] (Novoselov et al.).
- p. 4 left column, Rashba estimate
For Ez ∼50V/300nm[3] this gives λR ∼.5mK
- p. 4 reference list
[3] Y.K. Kato et al., Science 306, 1910 (2004).
- p. 1 introduction
The spin Hall effect has been observed in GaAs[3, 4]
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the 50 V / 300 nm gate geometry comes from the Novoselov et al. graphene device paper and not from Kato et al. Within the files: the page 4 image shows "50V/300nm[3]" as a bracketed citation; the reference list gives [3] as Kato et al. and [6] as Novoselov et al.; page 1 cites "observed in GaAs[3, 4]" and attributes the gated single-layer graphene films to [6]. So the paper's own usage makes [3] an unlikely source for a graphene gate field and [6] the likely intent, but only the authors can say. The λR estimate itself was not put in question.
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Wording The abstract says "the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed", but the body never discusses the chemical potential.
- p. 1 abstract
the effects of temperature, chemical potential, Rashba coupling, disorder and
- p. 1 abstract, last sentence
the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed
Judge's note: Read all four pages (text and page images). The body covers temperature (inelastic backscattering), the Rashba term, disorder, interactions and a parallel field H∥. The phrase "chemical potential" occurs only in the abstract; the nearest content is the Fig. 2 edge-population sketches and the remark on ambipolar gating, neither of which discusses an effect of chemical potential. Minor overstatement in the abstract.
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Wording The Laughlin-argument paragraph says "across the energy gap ∆so", whereas the paper elsewhere states "∆so leads to an energy gap 2∆so".
- p. 2 right column, Laughlin argument paragraph
across the energy gap ∆so it follows
- p. 2 left column, after Eq. (4)
∆so leads to an energy gap 2∆so
Judge's note: Page 2 image: left column gives the gap as 2Δso with E = ±sqrt((ħvFq)²+Δso²); right column says "cannot excite a particle across the energy gap Δso". Page 4 also quotes 2Δso ~ 2.4 K. Loose use of Δso as the gap scale; the meaning is not affected. Either form could be deliberate shorthand.
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Typo The gapless dispersion is printed "E(q) = ±vF |q|" without ħ, although Eq. (2) carries ħvF and the gapped dispersion on page 2 is ±sqrt((ħvF q)² + Δso²).
- p. 1 right column, after Eq. (2)
E(q) = ±vF |q|
- p. 2 left column, after Eq. (4)
(¯hvF q)2 + ∆2so
Judge's note: Page 1 image shows E(q) = ±v_F|q| directly after Eq. (2), which has −iħv_F. Page 2 image shows (ħv_F q)² + Δ²so under the root. The paper keeps ħ explicit elsewhere (ħvF/Δso, Δso/ħ), so the ħ is dropped in this one place. Evident fix: ±ħvF|q|. Cosmetic.
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Typo Missing word in the first sentence: "The generation of spin currents solid state systems has been a focus of intense recent interest" should read "spin currents in solid state systems".
- p. 1 first sentence of body
The generation of spin currents solid state systems has
- p. 1 first sentence
The generation of spin currents solid state systems
Judge's note: The page 1 image shows the sentence exactly as quoted, with no "in". Not an extraction artefact.
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Typo Misspellings: "gap semiconductor with quadradically dispersing bands" (should be quadratically); also in the acknowledgements "MRSEC grand DMR-00-79909" (should be grant).
- p. 2 left column, after Eq. (4)
gap semiconductor with quadradically dispersing bands
- p. 2 left column, after Eq. (4)
quadradically dispersing bands
- p. 1 first sentence
The generation of spin currents solid state systems
- p. 4 p4
microsopic SO interaction
Judge's note: Both are visible on the page images: "quadradically" on page 2, left column; "MRSEC grand" on page 4 acknowledgements. The other items bundled into this cluster are judged elsewhere: the missing "in" under C003 and "microsopic" under C015.
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Typo Duplicated word: "adiabatically insert a quantum φ = h/e of magnetic flux quantum down the cylinder" should read "a quantum φ = h/e of magnetic flux".
- p. 2 right column, Laughlin argument
adiabatically insert a quantum φ = h/e of
- p. 2 Laughlin argument
insert a quantum φ = h/e of
Judge's note: The page 2 image, right column, shows the phrase as quoted with "quantum" appearing twice. Cosmetic redundancy; the meaning is clear.
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Typo Fig. 1 caption begins "(a) One dimensional energy bands for a strip of graphene", but Fig. 1 is a single panel with an inset, and there is no (b).
- p. 3 Fig. 1 caption
(a) One dimensional energy bands for a strip of
- p. 3 Fig. 1 caption
FIG. 1: (a) One dimensional energy bands for a strip
- p. 3 FIG. 1 caption
(a) One dimensional energy bands
Judge's note: Page 3 image: Fig. 1 is one plot with an inset and no panel letters; the caption contains "(a)" and no "(b)". The (a)/(b) labels on the page belong to Fig. 2. A stray panel label; cosmetic.
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Typo Misspelling: "treating the microsopic SO interaction" should be "microscopic".
- p. 4 left column, before Eq. (7)
the microsopic SO interaction
- p. 4 before Eq. 7
microsopic SO interaction
- p. 4
treating the microsopic SO interaction
Judge's note: Page 4 image, left column before Eq. (7), shows "microsopic". The word is spelled correctly on page 1 ("microscopic SO interaction").
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Typo Doubled article on page 4: "and d is the a basis vector from a hexagon center"; one of "the" or "a" should be deleted.
- p. 4 left column, first-star approximation
and d is the a basis vector from a hexagon center
- p. 4 left column, first-star approximation
d is the a basis vector from a hexagon center
- p. 4 first-star approximation
d is the a basis vector
Judge's note: Read on the crop and the full page 4 image: the text prints "d is the a basis vector from a hexagon center to an A or B sublattice site". Two articles in a row; "a" is not a symbol here (it is upright text, not the italic lattice constant). Cosmetic.
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Typo Misspelling in the acknowledgements on page 4: "MRSEC grand DMR-00-79909" should read "MRSEC grant DMR-00-79909".
- p. 4 acknowledgements
MRSEC grand DMR-00-79909
Judge's note: Read on the crop and the full page 4 image: "supported by the NSF under MRSEC grand DMR-00-79909 and the DOE under grant DE-FG02-ER-0145118". The same sentence uses "grant" correctly a few words later. Cosmetic.
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Typo Misplaced closing parenthesis on page 4: "ported to the top (bottom contacts), generating" should read "top (bottom) contacts".
- p. 4 left column, first line of text
ported to the top (bottom contacts), generating
Judge's note: Read on the crop and the full page 4 image. The sentence starts at the foot of page 3 (text layer): "will be split, with the up (down) spins trans-" and continues "ported to the top (bottom contacts)". The parallel with "up (down) spins" shows the parenthesis should close after "bottom". Cosmetic; the meaning is clear.
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Typo Reference [8] prints the third author as "N.B. Brandt, S.M. Chudinov and Y.G. Ponomarav,"; the surname is probably "Ponomarev".
- p. 4 reference [8]
N.B. Brandt, S.M. Chudinov and Y.G. Ponomarav,
- p. 4 Ref. 8
Ponomarav
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the third author of "Semimetals 1. Graphite and its compounds" (North Holland, 1988) is Ya. G. Ponomarev. The page image does print "Ponomarav" in Ref. [8], but nothing in the files gives the correct spelling, so this cannot be verified here and is left as a query to the authors.
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Typo Reference formatting slips on page 4: Ref. [12] "Phys. Rev. Lett 49, 405" lacks the period after "Lett", and Ref. [13] "93, 206602(2004)" lacks the space before the year.
- p. 4 Ref. 12
Phys. Rev. Lett 49, 405
- p. 4 Ref. 13
93, 206602(2004)
Judge's note: Read on both crops and the full page 4 image. Ref. [12] prints "Phys. Rev. Lett 49, 405 (1982)" while Refs. [2], [5], [11], [13] and [21] print "Phys. Rev. Lett." with a period. Ref. [13] prints "206602(2004)" while the other entries have a space before the year. Both are present as described; purely punctuation and spacing inconsistencies in the reference list.
Second check: none (judge only)