Superconductivity in CoO$_2$ Layers and the Resonating Valence Bond Mean Field Theory of the Triangular Lattice t-J model

TL;DR

This paper applies RVB mean field theory to the triangular lattice in CoO$_2$ layers, revealing complex order parameters, the importance of hopping sign, and potential implications for superconductivity and Hall effect behavior.

Contribution

It introduces a detailed RVB mean field analysis of the triangular lattice t-J model, highlighting the role of hopping sign and explaining superconductivity in CoO$_2$ layers.

Findings

Order parameter is complex away from half filling.

Superconductivity's robustness depends on the sign of hopping.

High frequency Hall constant increases linearly with temperature.

Abstract

Motivated by the recent discovery of superconductivity in two dimensional CoO$_2$ layers, we present some possibly useful results of the RVB mean field theory applied to the triangular lattice. Away from half filling, the order parameter is found to be complex, and yields a fully gapped quasiparticle spectrum. The sign of the hopping plays a crucial role in the analysis, and we find that superconductivity is as fragile for one sign as it is robust for the other. Na$_x$CoO$_2\cdot y$H$_2$O is argued to belong to the robust case, by comparing the LDA Fermi surface with an effective tight binding model. The high frequency Hall constant in this system is potentially interesting, since it is pointed out to increase linearly with temperature without saturation for T $>$ T$_{degeneracy}$.