Pairing Properties of the $t$-$t^{\prime }$-$t^{\prime \prime }$-$J$ model

Abstract

We study the pairing properties of the two-dimensional $t$-$t^{\prime }$-$t^{\prime \prime }$-$J$ model, where $t^{\prime }$ and $t^{\prime \prime }$ are second and third neighbor hoppings, at a doping level $x\approx 0.1$. Recent studies of the $t$-$t^{\prime }$-$J$ model find strong pairing for $t^{\prime }>0$, associated with electron doping, but an absence of pairing for $t^{\prime }<0$ 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 $t^{\prime \prime }$ comparable to $t^{\prime }$, 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 ($t^{\prime }<0,t^{\prime \prime }>0$) while for the electron-doped system ($t^{\prime }>0,t^{\prime \prime }<0$) $d$-wave pairing is robust. Extended hoppings appear to be insufficient to make the one-band $t$-$t^{\prime }$-$J$ model capable of describing the pairing in the hole doped system.

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