Universal scaling in BCS superconductivity in three dimensions in non-$s$ waves

Abstract

The solutions of a renormalized BCS equation are studied in three space dimensions in $s$, $p$ and $d$ waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length $ξ$ and a large critical temperature, $T_c$, appropriate for some high-$T_c$ materials. The BCS gap, $T_c$, $ξ$ and specific heat $C_s(T_c)$ as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below $T_c$ in $p$ and $d$ waves.