Numerical extrapolation method for complex conductivity of disordered metals

Recently, quantum corrections to optical conductivity of disordered metals up to the UV region were observed. Although this increase of conductivity with frequency, also called anti-Drude behavior, should disappear at the electron collision frequency, such transition has never been observed, or described theoretically. Thus the knowledge of optical conductivity in a wide frequency range is of great interest. It is well known that the extrapolation of complex conductivity is ill-posed-a solution of the analytic continuation problem is not unique for data with finite accuracy. However, we show that assuming physically appropriate properties of the searched function a (co), such as symmetry, smoothness, and asymptotic solution for low and high frequencies, one can significantly restrict the set of solutions. We present a simple numerical method utilizing the radial basis function approximation and simulated annealing, which reasonably extrapolates the optical conductivity from visible frequency range down to the far-infrared and up to the ultraviolet region. The method was compared with two widely used analytic continuation techniques and resulting extrapolation obtained on MoC and NbN thin films was checked by transmission measurements across a wide frequency range.