Universal zero-frequency Raman slope in ad-wave superconductor

It is known that for a superconductor of a nodal gap, the in-plane microwave conductivity saturates at low temperatures to a universal value independent of the impurity concentration. We demonstrate that a similar feature can be accessed using channel-dependent Raman scattering. For a $d_{x^2-y^2}$-wave superconductor, the slope of low-temperature Raman intensity at zero frequency is found to be universal in the $A_{1g}$ and $B_{2g}$ channels, but not in the $B_{1g}$ channel. Moreover, universal Raman slopes are sensitive not only to the existence of a node, but also to different pairing states and should allow one to distinguish between such pairing states.