Pairing Symmetry and Upward Curvature of Upper Critical Field in Superconducting $Na_{0.35} Co O_2 \cdot y H_2 O$

TL;DR

This paper investigates the upward curvature of the upper critical field in hydrate cobaltate superconductors, attributing it to a transition between different pairing symmetries on separate energy bands, with s-wave to $d_{x^2-y^2}+ id_{xy}$ being the best fit.

Contribution

It introduces a microscopic model explaining the upward curvature as a transition between pairing symmetries, specifically from s-wave to $d_{x^2-y^2}+ id_{xy}$, in hydrate cobaltate superconductors.

Findings

Upward curvature results from pairing symmetry transition.

Transition from s-wave to $d_{x^2-y^2}+ id_{xy}$ fits experimental data.

Different pairing symmetries cause varying upward curvatures.

Abstract

The origin for the upward curvature of the upper critical field ($H_{c2}$) observed in hydrate cobaltate Na$_{0.35}$CoO$_{2} \cdot y$H$_{2}$O is investigated based on the microscopic gap equation. It is shown that the observed upward curvature results from the transition between two different pairing symmetries that occur on different energy bands. Furthermore, different pairing symmetries involved in the transition results in different upward curvatures. By considering transitions among all lowest possible pairing symmetries, it is found that the transition of the pairing symmetry from s-wave at low fields to $d_{x^2-y^2}+ id_{xy}$ at high fields is the best fit to the experimental data. Our results provide an important clue to the understanding of the superconductivity in hydrate cobaltate.