A numerical extrapolation method for complex conductivity of disordered metals

TL;DR

This paper introduces a numerical method combining radial basis functions and simulated annealing to extrapolate complex conductivity of disordered metals across a wide frequency spectrum, addressing the ill-posed nature of the problem.

Contribution

It presents a novel numerical approach for extrapolating optical conductivity in disordered metals using physically motivated constraints and advanced approximation techniques.

Findings

Successfully extrapolated conductivity for MoC and NbN films.

Validated extrapolation with transmission measurements across wide frequency range.

Revealed anti-Drude behavior in optical conductivity at high frequencies.

Abstract

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 behaviour, 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 $\sigma(\omega)$, 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 far infrared and up to ultraviolet region. Extrapolation obtained on MoC and NbN thin films was checked by transmission measurement across a wide frequency range.