Quantum Spin Hall Insulator State in HgTe Quantum Wells
Science, 2007 · paper · Physics
Reports transport measurements on HgTe/(Hg,Cd)Te quantum wells. Wells thicker than 6.3 nm show a residual conductance near 2e²/h that is independent of sample width and destroyed by a small magnetic field, which the authors present as evidence of the quantum spin Hall effect.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
1 finding
Reference or label Fig. 4 labels the dotted line at the plateau of trace I "G = 0.01 e²/h", but the line is drawn at about 1.7×10^7 Ω, which is about 0.0015 e²/h; 0.01 e²/h would be about 2.6 MΩ.
- p. 20 Fig. 4, label at dotted line on trace I
G = 0.01 e
- p. 9 body text, first paragraph
is at least several tens of MΩ
- p. 20 Fig. 4, label on dotted line at the plateau of trace I
G = 0.01 e² /h
- p. 20 Fig. 4, label upper left, curve I
G = 0.01 e /h
Only the authors can say what is right here.
Judge's note: Viewed the Fig. 4 page image. The dotted line beside the label "G = 0.01 e²/h" sits about a quarter of a decade above the 10^7 Ω tick, at roughly 1.7×10^7 Ω, and the plateau of trace I is at the same level. With h/e² ≈ 25.8 kΩ, 0.01 e²/h corresponds to 2.58 MΩ, almost a decade lower. The other two labels match their lines (0.3 e²/h ≈ 86 kΩ, 2 e²/h ≈ 12.9 kΩ). The page 9 text says the resistance is "at least several tens of MΩ" and that this is the noise floor, which agrees with the plotted level rather than the label. The label may be meant as a rough order-of-magnitude or upper-bound marker (about 0.001 e²/h would fit the line), so the authors should say which. The reviewers' side remark that "several tens of MΩ" differs from about 20 MΩ is only looseness of wording and is not confirmed as a defect.
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13 minor (typos and the like; most checked by the judge only)
Wording Methods list only a dilution refrigerator ("base temperature T < 30 mK") and a 4He cryostat with vector magnet ("T = 1.4 K, and fields up to 300 mT in variable direction"), yet the Fig. 4 inset is "a trace (in black) taken at 1.8 K"; the system used for the 1.8 K trace is not stated.
- p. 5 experimental description
(T = 1.4 K, and fields up to 300 mT in variable direction)
- p. 9 last paragraph
compare it with a trace (in black) taken at 1.8 K
- p. 11 Top line
≈0.7 T
- p. 5 Experimental description
fields up to 300 mT in variable direction
Judge's note: Verified on pages 5, 9, 16 and the Fig. 4 inset on page 20 (labelled T = 1.8 K). The 1.8 K temperature matches neither stated setup and the paper gives no explanation; a 4He cryostat can plausibly run at 1.8 K, so this is a minor unexplained inconsistency. The second reviewer note (0.7 T in-plane FWHM versus the 300 mT vector magnet) is the same point as C009 and is judged there.
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Wording In-plane width "(B∥FWHM ≈ 0.7 T)" is quoted alongside Fig. 5 data "obtained in the vector magnet system at 1.4 K", but that system is described as providing "fields up to 300 mT in variable direction" and Fig. 5 spans only about ±0.08 T; the source of the 0.7 T value is not stated.
- p. 11 first line
≈0.7 T
- p. 5 experimental description
fields up to 300 mT in variable direction
- p. 21 Fig. 5, x-axis range
0.05
Only the authors can say what is right here.
Judge's note: Verified on pages 5, 10, 11 and the Fig. 5 image on page 21. The Fig. 5 x-axis runs from about -0.08 to +0.08 T, and the 0° trace is essentially flat at about 0.14 e²/h over that range. An FWHM of 0.7 T needs half-maximum points near ±0.35 T, beyond the stated 300 mT maximum and far beyond the plotted range. The value may come from another magnet or from extrapolation; the paper does not say, so this is a query for the authors.
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Wording "We have observed this phenomenon in a number of samples in the inverted regime, with 6.5 nm < d < 12 nm" uses strict inequalities that exclude the 6.5 nm sample of Fig. 1 and the 12 nm experimental point in Fig. 3.
- p. 6 second paragraph, last sentence
with 6.5 nm < d < 12 nm
- p. 6 first line
Hall bar with a well width of 6.5 nm
- p. 19 Fig. 3, experimental open squares
12
- p. 19 Fig. 3, open red squares (experimental points)
inverted
Judge's note: Page 6 image shows the strict '<' signs. The phenomenon is illustrated on the 6.5 nm Hall bar (page 6, Fig. 1 caption). Fig. 3 (page 19) shows open red squares at about 6.4 to 6.5 nm, about 7.2 to 7.3 nm, and 12 nm. The stated sample range is "from 5.5 nm ... to 12 nm" (page 5). Almost certainly loose use of '<' for '≤'; the meaning is recoverable.
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Wording "R14,23 plateaus out at well below 100 kΩ (i.e., G14,23 = 0.3e2/h)": 0.3 e²/h corresponds to about 86 kΩ, and trace II in Fig. 4 peaks at about 9×10^4 Ω, so "well below 100 kΩ" is loose.
- p. 9 First paragraph
well below 100 kΩ (i.e., G14,23 = 0.3e2/h)
- p. 20 Fig. 4, trace II
G = 0.3 e²/h
Judge's note: Page 9 image confirms the wording. In Fig. 4 (page 20) trace II tops out just under the 10^5 Ω gridline, at the dotted G = 0.3 e²/h line. h/e² = 25.8128 kΩ, so 0.3 e²/h is about 86 kΩ, roughly 14% under 100 kΩ. The phrase may be meant relative to the tens-of-MΩ of trace I. A subjective wording point, not a numerical error.
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Wording Note 21 refers to "the d =7 nm, L = 20.0 µm devices", whereas the only inverted L = 20.0 µm devices described in the text and in the Fig. 4 and Fig. 5 captions have d = 7.3 nm.
- p. 14 Note 21
d =7 nm, L = 20.0 µm devices
- p. 9 first paragraph
but now contains a 7.3 nm wide
Only the authors can say what is right here.
Judge's note: Page 14 image shows "d =7 nm". Page 9 text and the page 16 captions give 7.3 nm for the (20.0 × 13.3) µm² inverted device. Fig. 3 (page 19) has experimental points near 7.2 to 7.3 nm and none at 7.0 nm. It could be a rounding or a different wafer; only the authors can say which.
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Wording Note 22 says "FWHM of the magnetoresistance peak is about 10 mT at 30 mK, increasing to 28 mT at 1.4 K", while the text it supports describes a "cusp-like conductance peak" and Fig. 5 plots conductance G (the feature is a dip in resistance).
- p. 14 Note 22
FWHM of the magnetoresistance peak
- p. 10 last paragraph
cusp-like conductance peak is observed for perpendicular
Judge's note: Verified on the page 14 and page 10 images and on Fig. 5 (page 21; y-axis G / e²/h, peak at B = 0). The main text also uses the term loosely ("Fig. 5 shows that the magnetoresistance is actually strongly anisotropic"), so this is loose terminology with a recoverable meaning.
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Typo Eq. 1 writes the dispersion term as "H = ϵ(k) + di(k)σi" while Eq. 2 defines it as "ϵk = C − D(kx² + ky²)" (function argument versus subscript).
- p. 3 Eq. 1
H = ϵ(k) + di(k)σi
- p. 4 Eq. 2
ϵk = C −D(k2
Judge's note: Checked on the page 3 and page 4 images: Eq. 1 has ε(k), Eq. 2 has ε with subscript k. Clearly the same object; purely a notational inconsistency.
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Typo "conductance" is printed where the conduction band is meant: "crossing of conductance- (HH1) and valence- (HH2) band derived Landau levels" (p. 8) and "deriving from the HH1 conductance and E1 valence band" (Fig. 3 caption, p. 16).
- p. 8 First paragraph
crossing of conductance- (HH1) and valence- (HH2) band derived Landau levels
- p. 16 Fig. 3 caption
HH1 conductance and E1 valence band
- p. 16 Fig. 3 caption
deriving from the HH1 conductance and E1 valence band
- p. 16 Fig. 3 caption
deriving from the HH1 conductance and E1 valence band occurs
Judge's note: Both wordings verified on the page 8 and page 16 images; the band paired with 'valence' is the conduction band, so this is a word slip. The reviewers' second claim, that the caption swaps E1 and HH1, is not upheld. In the inverted regime the paper itself says the s-like level lies below the p-like one (page 4), and the Fig. 3 inset shows HH1 above E1 for d > 6.3 nm. HH1 is therefore the conduction band and E1 the valence band there, as the caption says. Only the conductance/conduction wording is confirmed.
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Typo Note 12: "Similar mass domain walls have been proposed to occur in three-dimensional in PbTe/(Pb,Sn)Te heterostructures" has a stray second "in" (or a missing noun after "three-dimensional").
- p. 13 References and Notes, note 12
to occur in three-dimensional in
- p. 13 Note 12
occur in three-dimensional in
Judge's note: Read on the page 13 image; the text is exactly as quoted. Cosmetic copy-edit error.
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Typo Reference 11 gives the identifier as "arxiv: cond-mat/0705.1516", combining an old-style archive prefix with a new-style number.
- p. 13 Reference 11
arxiv: cond-mat/0705.1516
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that arXiv identifiers of the form YYMM.NNNN (in use from April 2007) carry no 'cond-mat/' prefix. The page 13 image shows the entry as quoted. The paper's own stamp on page 1 uses the new form, "arXiv:0710.0582v1 [cond-mat.mes-hall]". The cited work is still identifiable; cosmetic.
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Typo Reference 20: "Phys. Rev. Lett. 96, 76804 (2006)" gives a five-digit article number, where the other Physical Review entries in the list carry six digits (e.g. "047204", "045322", "035321").
- p. 14 Reference 20
Phys. Rev. Lett. 96, 76804 (2006)
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that Physical Review Letters article numbers are six digits, so the true number would be 076804. The page 14 image shows "96, 76804 (2006)". The same list keeps leading zeros in refs 8, 13 and 24, so the entry is at least internally inconsistent. A dropped leading zero; cosmetic.
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Typo Fig. 1 caption (B): "the red and green Hall resistance traces of Fig. A" should read Fig. 1A; the figure number is missing.
- p. 15 Fig. 1 caption, part (B)
red and green Hall resistance traces of Fig. A
- p. 15 Fig. 1 caption, (B)
Hall resistance traces of Fig. A.
- p. 15 Fig. 1 caption
Hall resistance traces of Fig. A
Judge's note: Page 15 image shows "Fig. A." as quoted. Elsewhere the paper writes "Fig. 1A" (pages 5 and 10). The intended target is obvious from context, so the pointer is incomplete but harmless.
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Typo Fig. 2 caption (D) reads "giving rise to the one pair of counter-propagating edge states"; the article "the" before "one pair" is awkward and probably stray.
- p. 15 Fig. 2 caption (D)
giving rise to the one pair of counter-propagating
Judge's note: Read the full page 15 image; the wording is printed as quoted in the last line of the page. It is a cosmetic wording point only. The phrase could be intentional ("the one pair" meaning the single pair), so either form could be legitimate.
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