Infrared Conductivity of Cuprate Metals: Detailed Fit Using Luttinger Liquid Theory

Measurements of infrared conductivity in the normal state of the cuprate layer metals show a characteristic behavior in the plane of the layers which is in essential agreement among many experiments. A simple parametrization of this behavior, proposed originally by Collins and Schlesinger, and exploited by N. Bontemps and her group, which gives an adequate fit over frequencies from a few hundred cm$^{-1}$ to $>5000 $ cm$^{-1}$, is that the phase angle of the complex conductivity is independent of frequency. This fit is shown to be a natural consequence of Luttinger Liquid theory with charge-spin separation, and determines the exponent of the singularity at the Fermi surface to be $\sim .15\pm .05$.