Plane-chain coupling in YBa$_{2}$Cu$_{3}$O$_{7}$ : impurity effect on the critical temperature

TL;DR

This study models impurity effects on the critical temperature in YBa2Cu3O7, revealing that the coupling between planes and chains results in a reduced sensitivity of Tc to impurities compared to standard d-wave models.

Contribution

It introduces a two-band model of YBCO with plane-chain coupling, showing a diminished impurity impact on Tc and a continuous transition between s-wave and d-wave behaviors.

Findings

Tc is less sensitive to impurities than in standard d-wave models.

Impurity effects mainly affect plane-plane and chain-chain scattering, which do not significantly reduce Tc.

The model predicts a continuous variation from s-wave to d-wave impurity sensitivity depending on parameters.

Abstract

We have studied the effect of impurities on $T_{c}$ for a model of YBCO involving pairing both in the CuO$_{2}$ planes and in the CuO chains. In this model pairing in the planes is due to phonons, while Coulomb repulsion induces in the chains an order parameter with opposite sign. Due to the anticrossing produced by hybridization between planes and chains, the order parameter changes sign on a single sheet of the Fermi surface resulting in nodes in the gap. We find that $T_{c}$ is much less sensitive to impurities than in standard d-wave models. One reason is that impurities produce essentially plane-plane and chain-chain scattering, which does not affect the critical temperature. $T_{c } $ is reduced by plane-chain scattering, which is smaller by a factor of order hybridization coupling over Fermi energy. In the specific case which we have studied in details and which reduces to the two-band model, we have found a further reduction of the sensitivity of $T_{c}$ to impurities with a behaviour which can vary continuously from s-wave like to d-wave like depending on the parameters. We expect a similar reduction to occur in the general case.