Microwave conductivity and superfluid density in strongly overdoped Tl 2 Ba 2 CuO 6+δ

We present measurements of the microwave surface impedance of the single-layer cuprate Tl${}_{2}$Ba${}_{2}$CuO${}_{6+\ensuremath{\delta}}$, deep in the overdoped regime, with ${T}_{c}\ensuremath{\approx}25$ K. Measurements have been made using cavity perturbation of a dielectric resonator at 17 discrete frequencies ranging from 2.50 to 19.16 GHz, and at temperatures from 0.12 to 27.5 K. From the surface impedance we obtain the microwave conductivity, penetration depth, and superfluid density. The superfluid density displays a strong linear temperature dependence from 2 to 14 K, indicative of line nodes in the energy gap. The microwave data are compared with theoretical predictions for a $d$-wave superconductor with pointlike impurities, with the conclusion that disorder in Tl${}_{2}$Ba${}_{2}$CuO${}_{6+\ensuremath{\delta}}$ acts predominantly in the weak-to-intermediate-strength scattering regime, and that small-angle scattering is important.