Pairing properties of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi><mml:mtext>−</mml:mtext><mml:msup><mml:mi>t</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mtext>−</mml:mtext><mml:msup><mml:mi>t</mml:mi><mml:mrow><mml:mo>″</mml:mo></mml:mrow></mml:msup><mml:mtext>−</mml:mtext><mml:mi>J</mml:mi></mml:math> model
Shengtao Jiang, D. J. Scalapino, Steven R. White
Abstract
We study the pairing properties of the two-dimensional $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model, where ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ are second and third neighbor hoppings, at a doping level $x\ensuremath{\approx}0.1$. Recent studies of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model find strong pairing for ${t}^{\ensuremath{'}}>0$, associated with electron doping, but an absence of pairing for ${t}^{\ensuremath{'}}<0$, associated with hole doping. This is in contrast to the cuprates, where the highest transition temperatures appear for hole doping. Model parametrizations for the cuprates estimate a ${t}^{\ensuremath{''}}$ comparable to ${t}^{\ensuremath{'}}$, 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 $({t}^{\ensuremath{'}}<0,{t}^{\ensuremath{''}}>0)$, while for the electron-doped system $({t}^{\ensuremath{'}}>0,{t}^{\ensuremath{''}}<0)$ $d$-wave pairing is robust. Extended hoppings appear to be insufficient to make the one-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model capable of describing the pairing in the hole-doped system.