Transition Temperature of Superconductivity in Sodium Tungsten Bronze -Theoretical Study Based on First-principles Calculations-

Abstract

Using first-principles calculations, we examine the transition temperature $T_{\mathrm{c}}$ of superconductivity in sodium tungsten bronze ( Na${}_x$WO${}_3$, where $x$ is equal to or less than unity ). Although $T_{\mathrm{c}}$ is relatively low $T_{\mathrm{c}}(<\sim 3\mathrm{K})$, it is interesting that its characteristic exponential dependence on $x$ has been experimentally observed at $\sim 0.2<x<\sim 0.4$. On the basis of the McMillan equation for $T_{\mathrm{c}}$ including the effect of plasmons, we succeed in reproducing the absolute values of $T_{\mathrm{c}}$ and its $x$ dependence. We also find that the plasmon effect is crucial for the estimation of $T_{\mathrm{c}}$ as well as phonons. Since the calculated $T_{\mathrm{c}}$ may not exceed $\sim 20$ K even for $x<\sim 0.1$, the superconductivity at a low $T_{\mathrm{c}}$ can be interpreted by the usual phonon mechanism, including the plasmon effect. On the other hand, a high $T_{\mathrm{c}}$ up to about 90 K, which is found on the surface of a Na${}_x$WO${}_3$ system at $x\sim 0.05$ by recent experiments, cannot be explained by our results. This discrepancy suggests that another mechanism is required to clarify the nature of the high-$T_{\mathrm{c}}$ superconductivity of Na${}_x$WO${}_3$.

arXiv comment5 pages, 5 figures

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