Comment on "Superconductivity in electron-doped layered TiNCl with variable interlayer coupling"

TL;DR

This paper refines the understanding of superconductivity in TiNCl compounds, emphasizing the role of interlayer interactions and Coulomb scattering, and provides a quantitative model for transition temperatures based on structural parameters.

Contribution

It introduces a model linking superconducting T$_C$ to interlayer Coulomb interactions and scattering effects, clarifying the mechanisms in TiNCl compounds.

Findings

Superconductivity involves interactions between chlorine layers and intercalant layers.

Optimal T$_C$ scales with the inverse of the transverse A$_x$-Cl separation distance.

Remote Coulomb scattering affects T$_C$, especially when the separation distance is small.

Abstract

In their article, Zhang et al. [Phys. Rev. B 86, 024516 (2012)] present a remarkable result for A$_x$(S)$_y$TiNCl compounds ($\alpha$-phase TiNCl partially intercalated with alkali A and optionally co-intercalated molecular species S), finding the superconducting transition temperature T$_C$ scales with $d$$^{-1}$, where the spacing $d$ between TiNCl layered structures depends on intercalant thickness. Recognizing that this behavior indicates interlayer coupling, Zhang et al. cite, among other papers, the interlayer Coulombic pairing mechanism picture [Harshman et al., J. Phys.: Condens. Matter 23, 295701 (2011)]. This Comment shows that superconductivity occurs by interactions between the chlorine layers of the TiNCl structure and the layers containing A$_x$, wherein the transverse A$_x$-Cl separation distance {\zeta} is smaller than $d$. In the absence of pair-breaking interactions, the optimal transition temperature is modeled by T$_{C0}$ $\propto$ ({\sigma}/$A$)$^{1/2}$$\zeta$$^{-1}$, where {\sigma}/$A$ is the fractional charge per area per formula unit. Particularly noteworthy are the rather marginally-metallic trends in resistivities of A$_x$(S)$_y$TiNCl, indicating high scattering rates, which are expected to partially originate from remote Coulomb scattering (RCS) from the A$_x$ ions. By modeling a small fraction of the RCS as inducing pair-breaking, taken to cut off exponentially with {\zeta}, observations of T$_C$ < T$_{C0}$ are quantitatively described for compounds with {\zeta} < 4 {\AA}, and T$_C$ $\approx$ T$_{C0}$ for Na$_{0.16}$(S)$_y$TiNCl with propylene carbonate and butylene carbonate co-intercalants for which {\zeta} > 7 {\AA}. Since a spatially separated alkali-ion layer is not formed in Li$_{0.13}$TiNCl, the observed T$_C$ of 5.9 K is attributed to an intergrowth phase related to TiN (T$_C$ = 5.6 K).