Self-consistent gauge-invariant theory of the in-plane infrared response of high- T_c cuprate superconductors

We report on results of our theoretical study of the in-plane infrared conductivity of the high-T_c cuprate superconductors using the model where charged planar quasiparticles are coupled to spin fluctuations. The computations include both the renormalization of the quasiparticles and the corresponding modification of the current-current vertex function (vertex correction), which ensures gauge invariance of the theory and local charge conservation in the system. The incorporation of the vertex corrections leads to an increase of the total intraband optical spectral weight (SW) at finite frequencies, a SW transfer from far infrared to mid infrared, a significant reduction of the SW of the superconducting condensate, and an amplification of characteristic features in the superconducting state spectra of the inverse scattering rate 1∕τ. We also discuss the role of self-consistency and propose an interpretation of a kink occurring in the experimental low temperature spectra of 1∕τ around 1000 cm⁻¹.