Superconductivity in CoO2_2 Layers and the Resonating Valence Bond Mean Field Theory of the Triangular Lattice t-J model

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$_{degeneracy}$.Comment: Published in Physical Review B, total 1 tex + 9 eps files. Erratum added as separate tex file on November 7, 2003, a numerical factor corrected in the erratum on Dec 3, 200

Phase separation and stripe formation in the 2D t-J model: a comparison of numerical results

We make a critical analysis of numerical results for and against phase separation and stripe formation in the t-J model. We argue that the frustrated phase separation mechanism for stripe formation requires phase separation at too high a doping for it to be consistent with existing numerical studies of the t-J model. We compare variational energies for various methods, and conclude that the most accurate calculations for large systems appear to be from the density matrix renormalization group. These calculations imply that the ground state of the doped t-J model is striped, not phase separated.Comment: This version includes a revised, more careful comparison of numerical results between DMRG and Green's function Monte Carlo. In particular, for the original posted version we were accidentally sent obsolete data by Hellberg and Manousakis; their new results, which are what were used in their Physical Review Letter, are more accurate because a better trial wavefunction was use