Suppression of superconductivity in high-$T_c$ cuprates due to nonmagnetic impurities: Implications for the order parameter symmetry

TL;DR

This study investigates how nonmagnetic impurities suppress superconductivity in high-$T_c$ cuprates, revealing the impact on order parameter symmetry and supporting $d_{x^2-y^2}$-wave as the primary pairing symmetry.

Contribution

The paper provides a self-consistent numerical analysis of impurity effects on superconducting order parameters, clarifying the symmetry differences in tetragonal and orthorhombic structures.

Findings

$d_{x^2-y^2}$-wave order parameter decreases linearly with impurity concentration

Superconductivity ceases at a critical impurity concentration $n_i^c \,=\ 0.1$

Orthorhombic anisotropy induces an additional s-wave component

Abstract

We studied the effects of nonmagnetic impurities on high-temperature superconductors by solving the Bogoliubov-de Gennes equations on a two-dimensional lattice via exact diagonalization technique in a fully self-consistent way. We found that s-wave order parameter is almost unaffected by impurities at low concentrations while $d_{x^2-y^2}$-wave order parameter exhibits a strong linear decrease with impurity concentration. We evaluated the critical impurity concentration $n_i^c$ at which superconductivity ceases to be 0.1 which is in good agreement with experimental values. We also investigated how the orthorhombic nature of the crystal structure affects the suppression of superconductivity and found that anisotropy induces an additional s-wave component. Our results support $d_{x^2-y^2}$-wave symmetry for tetragonal and $s+d_{x^2-y^2}$-wave symmetry for orthorhombic structure.