Modeling Intercalated Group-4-Metal Nitride Halide Superconductivity with Interlayer Coulomb Coupling

Abstract

Behavior consistent with Coulomb-mediated high-T${}_C$ superconductivity is shown to be present in the intercalated group-4-metal nitride halides A${}_x$(S)${}_y$MNX, where the MNX host (M = Ti, Zr, Hf; X = Cl, Br) is partially intercalated with cations A${}_x$ and optionally molecular species (S)${}_y$ in the van der Waals gap between the halide X layers, expanding the basal-plane spacing d. The optimal transition temperature is modeled by T${}_{C0}$ $\propto$ ζ${}^{-1}$(σ/$A$)${}^{1/2}$, where the participating fractional charge per area per formula unit σ/$A$ and the distance ζ, given by the transverse A${}_x$-X separation (ζ < d), govern the interlayer Coulomb coupling. From experiment results for β-form compounds based on Zr and Hf, in which concentrations x of A${}_x$ are varied, it is shown that σ = γ[v(x${}_{opt}$ $-$ x${}_0$)], where x${}_{opt}$ is the optimal doping, x${}_0$ is the onset of superconducting behavior, v is the A${}_x$ charge state, and γ = 1/8 is a factor determined by the model. Observations of T${}_C$ < T${}_{C0}$ in the comparatively more disordered α-A${}_x$(S)${}_y$TiNX compounds are modeled as pair-breaking by remote Coulomb scattering from the A${}_x$ cations, which attenuates exponentially with increasing ζ. The T${}_{C0}$ values calculated for nine A${}_x$(S)${}_y$MNCl compounds, shown to be optimal, agree with the measured T${}_C$ to within experimental error. The model for T${}_{C0}$ is also found to be consistent with the absence of high-T${}_C$ characteristics for A${}_x$MNX compounds in which a spatially separated intercalation layer is not formed.

12 pages, 2 figures

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