Pairing Properties of the $t$-$t'$-$t''$-$J$ model

TL;DR

This study investigates the pairing mechanisms in the two-dimensional $t$-$t'$-$t''$-$J$ model, revealing that extended hoppings do not reconcile the differences in pairing behavior between electron and hole doping in cuprates.

Contribution

The paper demonstrates that including second and third neighbor hoppings in the $t$-$t'$-$t''$-$J$ model does not resolve the discrepancy in pairing properties between electron and hole doping.

Findings

Pairing is strong for electron doping ($t'>0$) but suppressed for hole doping ($t'<0$).

Extended hoppings are insufficient to explain pairing in hole-doped cuprates.

The model's parameters do not align with experimental observations of high-temperature superconductivity in hole-doped cuprates.

Abstract

We study the pairing properties of the two-dimensional $t$-$t'$-$t''$-$J$ model, where $t'$ and $t''$ are second and third neighbor hoppings, at a doping level $x\approx0.1$. Recent studies of the $t$-$t'$-$J$ model find strong pairing for $t'>0$, associated with electron doping, but an absence of pairing for $t'<0$ associated with hole doping. This is in contrast to the cuprates, where the highest transition temperatures appear for hole doping. Model parameterizations for the cuprates estimate a $t''$ comparable to $t'$, which, in principle, might fix this discrepancy. However, we find that it does not; we observe a suppression of pairing for the hole-doped system ($t'<0, t''>0$) while for the electron-doped system ($t'>0, t''<0$) $d$-wave pairing is robust. Extended hoppings appear to be insufficient to make the one-band $t$-$t'$-$J$ model capable of describing the pairing in the hole doped system.