2H-NbSe2-xSx: Mixed-Chalcogen Superconductivity

• 2H-NbSe2-xSx is a layered dichalcogenide where random Se/S substitution preserves the hexagonal P6_3/mmc structure while modifying the normal-state band structure and superconducting properties.
• It demonstrates intrinsic two-gap superconductivity with distinct nodeless gaps, evidenced by transport and spectroscopic techniques, and shows enhanced critical fields exceeding weak-coupling limits.
• Se/S substitution actively suppresses long-range charge-density-wave order and, when combined with dilute Fe impurities, leads to an anomalously gapless superconducting state through overlapping YSR bound states.

2H-NbSe$_{2-x}$S$_x$ is a mixed-chalcogen layered dichalcogenide in the 2H polytype, spanning pure 2H-NbSe$_2$ at $x=0$, intermediate Se/S-substituted compositions, and the mixed-chalcogen analogue 2H-NbSeS at $x\approx 1$. Across this series, random Se/S substitution preserves the global hexagonal $P6_3/mmc$ structure while modifying the normal-state band structure, suppressing long-range charge-density-wave coherence, and reshaping the superconducting response to both nonmagnetic and magnetic disorder. Recent work has emphasized two closely related themes: first, that 2H-NbSeS realizes a fully gapped dirty-limit two-band superconductor with two nodeless gaps of different magnitudes; second, that in Fe-doped 2H-NbSe$_{2-x}$S$_x$, gapless superconductivity can emerge at remarkably low magnetic impurity concentrations once $x>0$ (Moreno et al., 1 Aug 2025, Yadav et al., 17 Jun 2026).

1. Structural framework and substitution series

2H-NbSe$_{2-x}$S$_x$0 crystallizes in the 2H polytype with hexagonal space group $_x$1. Each layer contains one Nb plane sandwiched between two Se/S planes, and the layers are weakly coupled by van der Waals forces (Moreno et al., 1 Aug 2025). This layered architecture is central to both the electronic anisotropy and the long-range spatial extent of impurity-induced states discussed later.

For the substitution series characterized by XRD and EDS, the reported lattice parameters evolve systematically with sulfur content:

$_x$2	$_x$3 (nm)	$_x$4 (nm)
0.0	0.34451	1.2542
0.2	0.34327	1.2506
0.4	0.34197	1.2474
0.6	0.34099	1.2423
0.8	0.33984	1.2387

The same measurements report $_x$5 K for $_x$6, $_x$7 K for $_x$8, $_x$9 K for $_2$0, $_2$1 K for $_2$2, and $_2$3 K for $_2$4 (Moreno et al., 1 Aug 2025). In a separate study of single-crystalline 2H-NbSeS, the material becomes superconducting below $_2$5 K with moderate magnetic anisotropy (Yadav et al., 17 Jun 2026). A plausible implication is that the superconducting transition temperature in this family is sensitive not only to nominal sulfur content but also to the disorder landscape and the experimental context used to define the compound.

Random Se/S occupation does not change the nominal electron count or the global $_2$6 symmetry in 2H-NbSeS, but it does introduce strong local potential fluctuations (Yadav et al., 17 Jun 2026). This distinction between preserved average crystallography and altered local electronic environment is a recurring feature of the series.

2. Electronic structure, charge-density-wave suppression, and nesting

The electronic structure evolves substantially under Se$_2$7S substitution. In pure 2H-NbSe$_2$8, density functional theory on a 5-layer slab with PBE + Grimme-D3 finds that the central Se-derived pocket at $_2$9 is nearly spherical and that the Nb-derived tubular pockets exhibit strong $x=0$0–$x=0$1 warping along $x=0$2, so that the $x=0$3–K–M and A–H–L dispersions differ (Moreno et al., 1 Aug 2025). For $x=0$4, the Nb sub-bands become more two-dimensional: $x=0$5-warping is strongly suppressed, the dispersions at $x=0$6–K–M and A–H–L become nearly identical, and the Se/S pocket shrinks slightly. As $x=0$7 increases up to $x=0$8, the normal-state DOS at $x=0$9 is reduced and van Hove singularities are smeared by substitutional disorder; a tight-binding model captures this trend (Moreno et al., 1 Aug 2025).

A complementary description is provided for 2H-NbSeS. In pristine 2H-NbSe$x\approx 1$0, an incommensurate CDW sets in below $x\approx 1$1 K, reconstructing large portions of the Fermi surface and opening a partial gap $x\approx 1$2 meV on nested bands around the K–M region. In 2H-NbSeS, random Se/S substitution destroys the phase coherence necessary for long-range CDW order without changing the nominal electron count or the global symmetry (Yadav et al., 17 Jun 2026). Experimentally, the absence of any anomaly in $x\approx 1$3 and the lack of superlattice Bragg reflections in XRD confirm CDW suppression; a Bloch–Grüneisen fit yields $x\approx 1$4, $x\approx 1$5 K, and $x\approx 1$6 (Yadav et al., 17 Jun 2026).

Within that same study, the three-sheet Nb-4d/Se-4p Fermi surface predicted by DFT for 2H-NbSe$x\approx 1$7—two cylindrical Nb-derived sheets at $x\approx 1$8-A and K-H plus a small Se-$x\approx 1$9 pocket at $P6_3/mmc$0—remains essentially unmodified except for the removal of CDW-induced backfolded replicas (Yadav et al., 17 Jun 2026). Taken together, the two studies indicate that Se/S substitution both suppresses CDW reconstruction and reshapes the detailed dispersion. This suggests that the relevant low-energy physics cannot be reduced either to a rigid-band picture or to disorder-averaged CDW phenomenology alone.

Scanning tunneling microscopy further resolves how the dominant in-gap scattering channels change with substitution. In pure NbSe$P6_3/mmc$1, in-gap conductance maps around isolated Fe impurities are dominated by the atomic lattice vector $P6_3/mmc$2 and the CDW vector $P6_3/mmc$3. For $P6_3/mmc$4, new wavevectors appear at biases of $P6_3/mmc$5–$P6_3/mmc$6 mV: $P6_3/mmc$7 and $P6_3/mmc$8 connect M–L points of the Nb Fermi surface, $P6_3/mmc$9 lies along $_{2-x}$0–M nesting of the hexagonal Nb pocket and is identified with the Johannes–Mazin nesting vector, and $_{2-x}$1 corresponds to near-circular scattering from the central Se/S pocket (Moreno et al., 1 Aug 2025). DFT correlates $_{2-x}$2 with flattened hexagonal segments, $_{2-x}$3 with the central pocket, and $_{2-x}$4 with M–L curvature. Extended Data 8 shows an exponential CDW peak decay, leading to the conclusion that S substitution decouples layers, suppresses long-range CDW coherence, and replaces pure CDW scattering with band-structure-specific nesting vectors that dominate pair-breaking quasiparticle interference (Moreno et al., 1 Aug 2025).

3. Multiband superconductivity in 2H-NbSeS

The superconducting state of 2H-NbSe$_{2-x}$5 has been the subject of sustained debate. Angle-resolved photoemission spectroscopy data have been interpreted as evidence for multiband superconductivity, whereas scanning tunneling microscope experiments have been interpreted in terms of strongly anisotropic single-band superconductivity, with the CDW mimicking multigap character by reconstructing the Fermi surface and modifying the superconducting gap distribution (Yadav et al., 17 Jun 2026). In 2H-NbSeS, where long-range CDW order is suppressed but the layered $_{2-x}$6 structure is preserved, the same issue can be examined with reduced CDW-related ambiguity.

Several probes converge on a fully gapped superconducting state with two nodeless gaps of different magnitudes in 2H-NbSeS (Yadav et al., 17 Jun 2026). The upper critical field $_{2-x}$7, determined by the 90%-onset criterion in $_{2-x}$8 for both $_{2-x}$9 and $_x$0, exhibits pronounced upward curvature that cannot be described within a single-band framework. A conventional single-band WHH fit fails at low temperature. By contrast, the dirty-limit two-band Usadel model of Gurevich captures the data through the implicit equation

$_x$1

with

$_x$2

and

$_x$3

Fitting yields, for $_x$4, $_x$5, $_x$6, $_x$7, and $_x$8; for $_x$9, $x>0$0, $x>0$1, $x>0$2, and $x>0$3 (Yadav et al., 17 Jun 2026). The zero-temperature critical fields extrapolate to $x>0$4 T and $x>0$5 T. Within anisotropic GL theory, these correspond to $x>0$6 nm, $x>0$7 nm, and $x>0$8 (Yadav et al., 17 Jun 2026). The in-plane upper critical field exceeds the weak-coupling Pauli limit, which the same study states as $x>0$9 T.

Independent thermodynamic and electrodynamic probes support the same two-gap interpretation. From lower-critical-field data, the superfluid density is modeled as

$_{2-x}$0

with

$_{2-x}$1

and

$_{2-x}$2

For $_{2-x}$3, the fit gives $_{2-x}$4, $_{2-x}$5, $_{2-x}$6, $_{2-x}$7, and $_{2-x}$8 Oe; for $_{2-x}$9, $_x$00, $_x$01, $_x$02, $_x$03, and $_x$04 Oe (Yadav et al., 17 Jun 2026). A single-gap model cannot reproduce the pronounced low-temperature upward curvature of $_x$05, whereas the two-gap form yields excellent agreement.

Tunnel-diode-oscillator penetration-depth measurements likewise require a two-gap description over the full temperature range. At low $_x$06, a single-gap expression,

$_x$07

gives $_x$08, but the full-range fit yields $_x$09, $_x$10, $_x$11, and $_x$12 (Yadav et al., 17 Jun 2026). Electronic specific heat at zero field is also described by a two-gap fit,

$_x$13

with extracted values $_x$14, $_x$15, $_x$16, and $_x$17 (Yadav et al., 17 Jun 2026). The normal-state fit yields $_x$18 and $_x$19 K, and only the $_x$20 fit captures both $_x$21 and the low-temperature behavior.

These results are interpreted as evidence that multiband pairing is intrinsic to the Nb-4d Fermi surface and not a CDW artifact in 2H-NbSeS (Yadav et al., 17 Jun 2026).

4. Extremely dilute magnetic disorder and gapless superconductivity

A distinct aspect of 2H-NbSe$_x$22S$_x$23 emerges when the system is doped with extremely dilute Fe impurities. In the STM study, samples with sulfur substitution $_x$24 were doped with Fe at $_x$25 at.%—approximately one Fe per 3,000 unit cells—and measured at $_x$26, down to below 100 mK (Moreno et al., 1 Aug 2025).

In clean 2H-NbSe$_x$27 ($_x$28) with Fe, the response is that expected for localized magnetic impurity states in a gapped superconductor: well-defined Yu–Shiba–Rusinov peaks appear at $_x$29, with $_x$30 meV, while the DOS at zero bias vanishes far from impurities (Moreno et al., 1 Aug 2025). For any $_x$31, however, the phenomenology changes qualitatively. At Fe concentrations as low as $_x$32–$_x$33 at.%, zero-bias conductance maps show a finite, spatially homogeneous DOS at $_x$34 even in regions many coherence lengths, $_x$35 nm, from any Fe. Tunneling spectra far from impurities evolve from a full gap with $_x$36 to $_x$37–$_x$38, normalized to the above-gap conductance, signaling gapless superconductivity (Moreno et al., 1 Aug 2025).

The reported threshold Fe concentration for the gapless state is $_x$39–$_x$40 at.%, which is far below the few-percent level normally required in conventional $_x$41-wave superconductors (Moreno et al., 1 Aug 2025). The same study explicitly contrasts this with the few-percent threshold for gapless behavior in bulk conventional $_x$42-wave systems discussed by Shiba and by Hauser et al. This constitutes the central anomaly of the series: apparently negligible magnetic-impurity densities can produce a bulk-like finite DOS at the Fermi level once Se/S substitution is present.

The spatial homogeneity of the zero-bias DOS is particularly significant. The measurements show that the finite $_x$43 DOS is not confined to local impurity neighborhoods but persists many coherence lengths from identifiable Fe sites (Moreno et al., 1 Aug 2025). This suggests a collective impurity-band or overlap mechanism rather than a simple superposition of isolated in-gap bound states.

5. Microscopic modeling of disorder, impurity states, and in-gap scattering

The theoretical description of the gapless state uses a real-space BCS Hamiltonian on a triangular Nb lattice with hopping up to fifth nearest neighbors,

$_x$44

and chemical potential $_x$45 meV (Moreno et al., 1 Aug 2025). Magnetic impurities are modeled as local exchange potentials $_x$46 at random sites $_x$47, while nonmagnetic Se–S disorder is represented by local repulsive potentials $_x$48 at random sites $_x$49. In the Nambu basis $_x$50, the BdG Hamiltonian is

$_x$51

The gap is determined self-consistently through

$_x$52

with $_x$53 meV chosen so that the homogeneous $_x$54 meV. The local DOS is

$_x$55

using $_x$56 as numerical broadening (Moreno et al., 1 Aug 2025).

The key BdG result is that even at $_x$57 up to $_x$58–$_x$59 at.% and $_x$60 up to $_x$61, dilute magnetic and nonmagnetic disorder cooperate to fill in the gap, producing finite $_x$62 and six-fold-smeared YSR states (Moreno et al., 1 Aug 2025). The experimentally observed finite zero-energy DOS appears already at $_x$63–$_x$64 at.%, while theoretically comparable values require $_x$65–$_x$66 at.%; the study nonetheless emphasizes that both concentrations remain extremely small (Moreno et al., 1 Aug 2025).

The proposed origin of this high sensitivity is that YSR bound states in layered TMDs have long real-space tails, with $_x$67 a few nm. These tails overlap at very low impurity densities and, together with S-induced band-structure changes, generate a homogeneous in-gap background (Moreno et al., 1 Aug 2025). This mechanism links the disorder response to low dimensionality and to the material-specific Fermi surface rather than to impurity concentration alone.

The same framework is supported by the in-gap QPI data. In pure NbSe$_x$68, impurity scattering is dominated by $_x$69 and $_x$70, whereas for $_x$71 the dominant in-gap wavevectors are $_x$72–$_x$73, which trace nesting and curvature of the modified Nb and Se/S pockets (Moreno et al., 1 Aug 2025). The conclusion is that pair breaking for $_x$74 is dictated by substitution-modified band structure rather than by the dominant CDW interactions of pure 2H-NbSe$_x$75.

6. Comparison with pure 2H-NbSe$_x$76 and broader implications

Relative to representative literature values for pure 2H-NbSe$_x$77, the 2H-NbSeS study reports $_x$78 K rather than $_x$79 K, $_x$80 Oe rather than $_x$81 Oe, $_x$82 Oe rather than $_x$83 Oe, $_x$84 T rather than $_x$85 T, and $_x$86 T rather than $_x$87 T (Yadav et al., 17 Jun 2026). The coherence lengths remain similar, $_x$88 nm and $_x$89 nm versus literature values $_x$90 nm and $_x$91 nm, while the anisotropy remains close to $_x$92–$_x$93. The large diffusivity ratio, however, changes substantially: the literature value for pure 2H-NbSe$_x$94 is approximately $_x$95–$_x$96, whereas 2H-NbSeS gives $_x$97–$_x$98, which is described as strongly dirty (Yadav et al., 17 Jun 2026).

The same comparison emphasizes several trends upon Se$_x$99S substitution: suppression of CDW entirely, removal of Fermi-surface reconstruction and CDW-induced gap anisotropy, modest reduction of $_2$00, increased residual scattering rate, enhancement of $_2$01 above the weak-coupling Pauli limit, and robust two-gap ratios and weights (Yadav et al., 17 Jun 2026). In that view, multiband pairing is an intrinsic property of the Nb-4d-derived electronic structure.

The Fe-doped study extends the significance of the substitution series beyond multiband phenomenology. It demonstrates that even extremely dilute magnetic moments can render an $_2$02-wave state gapless in the presence of nonmagnetic substitutional disorder if the normal-state band structure favors extended impurity states and nesting (Moreno et al., 1 Aug 2025). This is presented as evidence for the inadequacy of Anderson’s theorem once realistic band structures and low-dimensionality effects are included. The same work further suggests that the robustness of superconducting gaps in other layered TMDs, and by extension 2D superconductors, must be reassessed by incorporating material-specific DFT dispersions and the interplay of CDW, electron–phonon coupling, and magnetic correlations (Moreno et al., 1 Aug 2025).

A common misconception is that random chalcogen substitution merely adds nonmagnetic disorder while leaving superconductivity qualitatively conventional. The available results point instead to a more specific conclusion. In 2H-NbSe$_2$03S$_2$04, Se/S substitution suppresses long-range CDW order, alters dimensionality and nesting, produces strong band-dependent scattering, and changes how dilute magnetic moments couple to the condensate (Moreno et al., 1 Aug 2025, Yadav et al., 17 Jun 2026). This suggests that the series is best understood not as a simple disorder-broadened version of 2H-NbSe$_2$05, but as a platform in which band-structure engineering and disorder cooperate to expose both intrinsic multiband superconductivity and an unusual route to gapless superconductivity.