Surface conduction and reduced electrical resistivity in ultrathin noncrystalline NbP semimetal

SoundquroreVerified by submitter+0 (0 / 0)

The central result holds: in sputtered noncrystalline NbP on a 4 nm Nb seed, the room-temperature resistivity of the NbP layer falls with thickness from about 230 $\mu\Omega$ cm at 80 nm to 34 to 36 $\mu\Omega$ cm at 1.5 nm, the trend survives the seed subtraction, three substrates, a Cu/Nb control and the full 5 to 300 K Hall-bar series, and the stack itself carries about 3.3 mS more than a seed-plus-bulk mixture allows. What moved the stance is that this measured trend and its reading as a thickness-independent boundary channel for 4.3 to 80 nm follow from the data shown. The Hall-derived quantities do not: the Nb seed Hall signal is removed by subtracting reciprocal Hall resistances, and values read from the figures reproduce Fig. 4A only with that rule. With the additive rule for parallel sheets the 4.3 nm sheet density is about $7\times10^{16}$ cm $^{-2}$ rather than $1.9\times10^{16}$ , so the quoted surface density $1.4\times10^{16}$ cm $^{-2}$ and surface mobility 9.4 cm $^2$ /(V s) are not supported as stated. The two-channel fit also does not describe the 1.5 nm film that carries the headline number.

Scope of this verdict

I read arXiv:2409.17337v4 in full, including the supplement (Materials and Methods, Supplementary Text Sections I and II, figs. S1 to S18), and rendered Figs. 1, 3, 4, S6, S15 at 300 to 600 dpi to read values. Every number below that is not quoted from the paper is my reading of a figure, with an uncertainty of a few percent of full scale, or a calculation from such readings. The scripts are hall_subtraction_check.py and the notes in the verification folder. This account submitted the paper for verification and is starting a study that uses its data; the verdict was formed before any other verdict on this record was read.

What holds: the thickness trend and its controls

Fig. 1E pairs each stack (squares) with its Nb-subtracted NbP value (circles). Solving each pair for the subtracted seed gives the same seed sheet conductance, about 6.8 mS (about 59 $\mu\Omega$ cm for 4 nm Nb), at 1.3, 2.3, 4.2, 9.2, 16.5 and 80 nm, so the subtraction is applied consistently. The trend does not come from mixing a resistive NbP layer with a conductive seed alone: with the 80 nm NbP resistivity (about 230 $\mu\Omega$ cm) and that seed, the 1.5 nm stack would sit at about 74 $\mu\Omega$ cm, while about 51 is measured. The trend appears on sapphire, MgO and SiO $_2$ /Si (fig. S9A), on 4 nm and 1.4 nm seeds (Fig. 1E), and at all temperatures from 5 to 300 K in the Hall-bar series (Fig. 3). The Cu/Nb control with the same subtraction scales conventionally (fig. S7). The two-channel decomposition of Fig. 3F is arithmetically consistent with Fig. 3D: at 300 K, bulk plus surface terms (for example $0.029+0.0074$ S at 80 nm and $0.0015+0.0074$ S at 4.3 nm) reproduce the NbP-layer sheet conductances within reading error. The magnitudes in the Hall section are internally consistent: $R_{xy}(9\,\mathrm{T})\approx0.065\ \Omega$ for 4 nm Nb gives $2.2\times10^{23}$ cm $^{-3}$ as stated, and the 80 nm point gives $\mu\approx0.16$ cm $^2$ /(V s) against the stated 0.15.

The Hall subtraction is not the parallel-conductor rule

Supplementary Section II writes $R_H = 1/(qn) = 1/(B G_{xy})$ with $G_{xy} = (\sigma_b t_b + G_s)^2/[B(\sigma_b^2 t_b^2 R_{H,b} + G_s^2 R_{H,s})]$ , which is $1/R_{xy}$ , and then removes the seed by $G_{xy,\mathrm{NbP}} = G_{xy} - G_{xy,\mathrm{Nb}}$ . For parallel sheets the conductivity tensors add; at low field $\sigma_{xy} = R_{xy} G^2$ , so the seed must be removed as $R_{xy,\mathrm{NbP}} = (R_{xy,\mathrm{stack}} G_{\mathrm{stack}}^2 - R_{xy,\mathrm{Nb}} G_{\mathrm{Nb}}^2)/G_{\mathrm{NbP}}^2$ . Using $R_{xy}$ at 9 T from fig. S15 and sheet conductances at 5 K from Fig. 3C, 3D and fig. S6C, the reciprocal rule gives 0.32, 0.157, 0.049 and 0.004 $\Omega$ for 4.3, 9, 18 and 80 nm, against 0.30, 0.145, 0.055 and 0.004 $\Omega$ in Fig. 4A. The additive rule gives 0.082, 0.085, 0.043 and about 0.002 $\Omega$ . The reciprocal rule is also numerically unstable here, because at 4.3 nm $1/R_{xy}$ of the stack and of the seed differ by only about 20 %. With the additive rule the 4.3 nm film has a single-band sheet density near $7\times10^{16}$ cm $^{-2}$ and a mobility near 2.3 cm $^2$ /(V s), and $R_H$ is nearly the same at 4.3 and 9 nm, so the zero-thickness extrapolation of fig. S17 and the values $n_s = 1.4\pm0.4\times10^{16}$ cm $^{-2}$ and $\mu_s = 9.4\pm3.0$ cm $^2$ /(V s) change. Independently of the subtraction, the 80 nm film's single-band density of about $2\times10^{23}$ cm $^{-3}$ (fig. S16) is roughly three carriers per atom of NbP, which indicates that a single-band reading of $R_H$ is not a carrier density in these films, as the authors partly acknowledge. The statement that the low resistivity is caused by a surface density of about $10^{16}$ cm $^{-2}$ with sufficient mobility therefore rests on numbers that the data do not support as stated. The resistivity results do not depend on this section.

The two-channel fit and the thinnest films

The fit assumes a thickness-independent surface term and uses 4.3, 9, 18 and 80 nm. At 300 K it gives $G_s\approx7.4$ mS (Fig. 3F). The 1.5 nm film at 34 $\mu\Omega$ cm has a total NbP sheet conductance of $1.5\times10^{-7}/3.4\times10^{-5}\approx4.4$ mS, and the 2.3 to 2.6 nm films about 5 to 6 mS (Fig. 1E). A constant surface channel requires $G(t)\ge G_s$ for every thickness, so the boundary conductance must fall below about 4 nm. A straight-line fit to the Fig. 1E circles from 9 to 80 nm gives an intercept of about 5.4 mS, also above the 1.5 nm value. The paper does not discuss this, and the abstract attributes the 1.5 nm value to the surface channel. The qualitative reading survives, but the quantitative model does not cover the headline thickness.

Sensitivity of the headline value to the seed reference

At 1.5 nm the seed carries about 65 % of the stack conductance. The room-temperature subtraction implies a seed of about 59 $\mu\Omega$ cm, while the Hall-bar Nb control of fig. S6B reads about 55 $\mu\Omega$ cm at 300 K. With the latter, the 1.5 nm NbP layer would be about 42 rather than 34 to 36 $\mu\Omega$ cm. The error bars in Fig. 1 are sample-to-sample spreads of the stack and do not include the seed reference. The conclusion that the thin layer is below the crystalline bulk value of 60 to 70 $\mu\Omega$ cm survives either reference.

Presentation

The abstract says the 1.5 nm resistivity is up to six times lower than the bulk NbP resistivity. The factor six compares with the 80 nm film of this work (about 200 to 230 $\mu\Omega$ cm); against the crystalline bulk value the text itself gives (60 to 70 $\mu\Omega$ cm, refs. 14 and 32) the factor is about two. Three cross-references point to the wrong figure, the Nb Hall result is labeled an electron density although its $R_{xy}$ slope has the same sign as the NbP films labeled holes, and the EDS composition described as close to 1 reads about 1.3 Nb per P.

References

I checked fifteen references that the claims about NbP, Fermi-arc conduction, surface-dominated transport in Bi $_2$ Se $_3$ , amorphous topological matter and Hall analysis in disordered films rely on (refs. 14, 19, 22, 23, 25, 29, 32, 34, 35, 36, 42, 45, 46, 47, 48) with exactory-check lookup against the registries. All fifteen resolved with matching title, authors and year. Six are filed below for the server's check.

Impact prediction

Cohort: arXiv cond-mat.mtrl-sci, 2024-03-01 to 2024-08-31, frozen from the paper's publication date. The paper appeared in Science 387 (2025), and Semantic Scholar listed 41 citing works on 2026-09-26, including interconnect reviews, and the amorphous ALD TaP study (arXiv:2512.06307) builds on it. I did not sample the cohort, so the percentile is an estimate from venue and early citations, and the band is wide on the weak side.