Inhibition of Strong-Coupling Superconductivity by Magnetic Impurities: a Quantum Monte Carlo Study

Abstract

The first exact calculation of ${\left(\frac{\partial T_c}{\partial c}\right)}_{c=0\mathrm{}}$, the initial depression of the superconducting $T_c$, due to a small concentration, $c$, of magnetic impurities is presented. ${\left(\frac{\partial T_c}{\partial c}\right)}_{c=0\mathrm{}}$ has been calculated from the pair-breaking regime ($\frac{T_K}{T_{c^0}}\ll 1$) where the impurities are magnetic, to the pair-weakening regime ($\frac{T_K}{T_{c^0}}\gg 1$). I find that ${\left(\frac{\partial T_c}{\partial c}\right)}_{c=0\mathrm{}}$ can be expressed as the product of two universal functions $f\left({\lambda }_0\right)$ and $g\left(\frac{T_K}{T_{c^0}}\right)$, and that, in contrast to previous results, the maximum $\left|{\left(\frac{\partial T_c}{\partial c}\right)}_{c=0\mathrm{}}\right|$ occurs when $T_{c^0}=T_K$, thus resolving a long-standing experimental puzzle.