Correlation between Superconducting Transition Temperature $T_c$ and Increase of Nuclear Spin-Lattice Relaxation Rate Devided by Temperature $1/T_1T$ at $T_c$ in the Hydrate Cobaltate Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O

TL;DR

This study investigates the relationship between the superconducting transition temperature and the increase in nuclear spin-lattice relaxation rate in hydrate cobaltates, revealing that higher $T_c$ correlates with greater DOS increase above $T_c$ and two-dimensionality.

Contribution

It provides new insights into how the increase in DOS just above $T_c$ relates to superconductivity in hydrate cobaltates, emphasizing the role of two-dimensionality.

Findings

Higher $T_c$ samples show larger $1/T_1T$ increase above $T_c$

Residual DOS in the SC state is larger in lower $T_c$ samples

The increase in DOS is linked to the two-dimensionality of the CoO$_2$ plane

Abstract

We have performed Co-nuclear quadrupole resonance (NQR) studies on Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O compounds with different Na ($x$) and hydrate ($y$) contents. Two samples with different Na contents but nearly the same $T_c$ values ($x$ = 0.348, $T_c$ = 4.7 K ; $x$ = 0.339, $T_c$ = 4.6 K) were investigated. The spin-lattice relaxation rate $1/T_1$ in the superconducting (SC) and normal states is almost the same for the two samples except just above $T_c$. NQR measurements were also performed on different-hydrate-content samples with different $T_c$ values, which were prepared from the same Na-content ($x$ = 0.348) sample. From measurements of $1/T_1$ using the different-hydrate-content samples, it was found that a low-$T_c$ sample with $T_c = 3.9$ K has a larger residual density of states (DOS) in the SC state and a smaller increase of $1/T_1T$ just above $T_c$ than a high-$T_c$ sample with $T_c$ = 4.7 K. The former behavior is consistent with that observed in unconventional superconductors, and the latter suggests the relationship between $T_c$ and the increase in DOS just above $T_c$. This increase, which is seemingly associated with the two-dimensionality of the CoO$_2$ plane, is considered to be one of the most important factors for the occurrence of superconductivity.