Figure 5: Frequency dependence of the conductivity of a superconductor at different temperatures relative to the transition temperature . (a) The real part exhibits a sharp drop at the superconducting gap and vanishes below for . For finite temperatures, the gap gradually moves to lower frequencies; in addition a finite conductivity emerges at low frequencies that increases considerably as ; even exceeds the normal state conductivity in a narrow frequency range right below . (b) The imaginary part of the conductivity diverges for low temperatures as . The kink of at also shows up in the imaginary part [46].