Impurity-induced $T_c$ reduction in high-temperature superconductors

We study the effects of nonmagnetic impurities substituted for Cu atoms on the superconducting transition temperature $T_c$ in high-temperature cuprate superconductors, using the $d\text{−}p$ model within the fluctuation exchange approximation and the coherent potential approximation. $T_c$ near the optimum-doped region reduces more rapidly than that for the over-doped region. We show that the rapid reduction of $T_c$ is due mainly to the damping of the quasiparticle in our formalism.

Figure 1

Calculated $T_c$ as functions of (a) the doping concentration $\delta$ and (b) the impurity concentration $n_i$. $T_c^0$ is the superconducting transition temperature for $n_i=0$.

Figure 2

Imaginary part of the dynamical susceptibility for various impurity concentrations, at each ${\mathbf{Q}}_{\mathrm{inc}}$ where the incommensurate AF peak appears. $T=T_c^0$.

Figure 3

Imaginary part of the self-energy of the quasiparticle at $\mathbf{k}=(14\pi ∕16,2\pi ∕16)$ for various impurity concentrations. $T=T_c^0$.