Hole-pair symmetry and excitations in the strong-coupling extendedt−Jzmodel: competition betweend-wave and

Abstract

We analytically calculate the ground state pairing symmetry and excitation spectra of two holes doped into the half-filled t − t ′ − t ′′ − Jz model in the strong-coupling limit (Jz >> |t|, |t ′ |, |t ′′ |). In leading order, this reduces to the t ′ − t ′′ − Jz model, where there are regions of d-wave, s-wave, and (degenerate) p-wave symmetry. We find that the t − Jz model maps in lowest order onto the t ′ − t ′′ − Jz model on the boundary between d and p symmetry, with a flat lower band in the pair excitation spectrum. In higher order, d-wave symmetry is selected from the lower pair band. However, we observe that the addition of the appropriate t ′ < 0 and/or t ′′ > 0, the signs of t ′ and t ′′ found in the hole-doped cuprates, could drive the hole-pair symmetry to p-wave, implying the possibility of competition between p-wave and d-wave pair ground states. (An added t ′ > 0 and/or t ′′ < 0 generally tend to promote d-wave symmetry.) We perturbatively construct an extended quasi-pair for the t − Jz model. In leading order, there are contributions from sites at a distance of √ 2 lattice spacings apart; however, contributions from sites 2 lattice spacings apart, also of the same order, vanish identically. Finally, we compare our approach with analytic calculations for a 2 × 2 plaquette and with existing numerical work, and discuss possible relevance to the physical parameter regime.

Unfrustrating the t-J Model: Exact d-wave BCS Superconductivity in the t'-J_z-V Model

“…This state is unphysical because it has an infinite energy density when the 1/r Coulomb repulsion is not ignored 2. The t-t -t -Jz model has been studied in Ref [25,26]…”