Superconductivity in Na$_x$CoO$_2$$\cdot$yH$_2$O : Is Spin-Charge Separation Protecting a d$_1$+id$_2$ State ?

TL;DR

This paper investigates the superconducting state in Na$_x$CoO$_2$$ullet$yH$_2$O, proposing that spin-charge separation may protect a d$_1$+id$_2$ wave state from disorder effects, unlike p or d-wave states.

Contribution

It introduces the idea that spin-charge decoupling acts as a quantum protectorate, safeguarding a specific d-wave superconducting state against disorder.

Findings

Disorder from Na$^+$ vacancies destroys p or d-wave superconductivity.

Experimental robustness suggests a spin-charge decoupling mechanism.

Calculated Knight shift and ${1ackslash T}_1$ align with RVB theory predictions.

Abstract

Superconductivity in Na$_x$CoO$_2$$\cdot$yH$_2$O is likely to be a p or d-wave; however, experiments are unable to pinpoint the symmetry. A simple estimate of pair breaking effects from an unavoidable `Na$^+$ vacancy disorder' in an ordered Na$^+$ lattice, at an optimal $x_{\rm opt} \approx 0.30$ is shown to destroy a Fermi liquid based p or d-wave superconductivity. However, a robustness of superconducting and normal states, seen in experiments is pointed out and argued to imply presence of a `quantum protectorate', possibly a `spin-charge decoupling' that protects a d$_1$+id$_2$ and not a p-state. A calculation of Knight shift and ${1\over T_1}$ in the framework of RVB mean field theory and a fit to the data of Kobayashi ${\it et al.}$ [9] is made.