We argue that recent measurements on both the superfluid density and the optical conductivity of high-quality ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) films can be understood almost entirely within the theory of disordered BCS $d$-wave superconductors. The large scattering rates deduced from experiments are shown to arise predominantly from weak scatterers, probably the Sr dopants out of the ${\mathrm{CuO}}_2$ plane, and correspond to a significant suppression of $T_c$ relative to a pure reference state with the same doping. Our results confirm the “conventional” viewpoint that the overdoped side of the cuprate phase diagram can be viewed as approaching the BCS weak-coupling description of the superconducting state, with significant many-body renormalization of the plasma frequency. They suggest that, while some of the decrease in $T_c$ with overdoping may be due to weakening of the pairing, disorder plays an essential role.

• Received 16 March 2018
• Revised 6 June 2018

DOI:https://doi.org/10.1103/PhysRevB.98.054506