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Register a new userTransition Temperature of Superconductivity in Sodium Tungsten Bronze -Theoretical Study Based on First-principles Calculations-
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Using first-principles calculations, we examine the transition temperature $T_{rm c}$ of superconductivity in sodium tungsten bronze ( Na$_x$WO$_3$, where $x$ is equal to or less than unity ). Although $T_{rm c}$ is relatively low $T_{rm c}( <sim 3 {rm K})$, 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 $T_{rm c}$ including the effect of plasmons, we succeed in reproducing the absolute values of $T_{rm c}$ and its $x$ dependence. We also find that the plasmon effect is crucial for the estimation of $T_{rm c}$ as well as phonons. Since the calculated $T_{rm c}$ may not exceed $sim 20$ K even for $x <sim 0.1$, the superconductivity at a low $T_{rm c}$ can be interpreted by the usual phonon mechanism, including the plasmon effect. On the other hand, a high $T_{rm c}$ up to about 90 K, which is found on the surface of a Na$_x$WO$_3$ system at $xsim 0.05$ by recent experiments, cannot be explained by our results. This discrepancy suggests that another mechanism is required to clarify the nature of the high-$T_{rm c}$ superconductivity of Na$_x$WO$_3$.
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We theoretically study superconductivity in UTe$_2$, which is a recently-discovered strong candidate for an odd-parity spin-triplet superconductor. Theoretical studies for this compound faced difficulty because first-principles calculations predict an insulating electronic state, incompatible with superconducting instability. To overcome this problem, we take into account electron correlation effects by a GGA$+U$ method and show the insulator-metal transition by Coulomb interaction. Using Fermi surfaces obtained as a function of $U$, we clarify topological properties of possible superconducting states. Fermi surface formulas for the three-dimensional winding number and three two-dimensional $mathbb{Z}_2$ numbers indicate topological superconductivity at an intermediate $U$ for all the odd-parity pairing symmetry in the $Immm$ space group. Symmetry and topology of superconducting gap node are analyzed and the gap structure of UTe$_2$ is predicted. Topologically protected low-energy excitations are highlighted, and experiments by bulk and surface probes are proposed to link Fermi surfaces and pairing symmetry. Based on the results, we also discuss multiple superconducting phases under magnetic fields, which were implied by recent experiments.
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