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The microwave surface impedance measurements on cuprate superconductorsprovide the crucial information of the effect of the impurity scattering on thequasiparticle transport, however, the full understanding of the effect of theimpurity scattering on the quasiparticle transport is still a challengingissue. Here based on the microscopic octet scattering model, the effect of theimpurity scattering on the low-temperature microwave conductivity in cupratesuperconductors is investigated in the self-consistent $T$-matrix approach. Theimpurity-dressed electron propagator obtained in the Fermi-arc-tipapproximation of the quasiparticle excitations and scattering processes isemployed to derive the electron current-current correlation function by takinginto account the impurity-induced vertex correction. It is shown that themicrowave conductivity spectrum is a non-Drude-like, with a sharp cusp-likepeak extending to zero-energy and a high-energy tail falling slowly withenergy. Moreover, the microwave conductivity decreases with the increase of theimpurity concentration or with the increase of the strength of the impurityscattering potential. In a striking contrast to the dome-like shape of thedoping dependence of the superconducting transition temperature, the microwaveconductivity exhibits a reverse dome-like shape of the doping dependence. Thetheory also show that the highly unconventional features of the microwaveconductivity are generated by both the strong electron correlation andimpurity-scattering effects.

Microwave conductivity due to impurity scattering in cuprate superconductors