A numerical extrapolation method for complex conductivity of disordered metals

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.

arXiv comment10 pages, 7 figures

References in corpus (9)

• Kramers-Kronig constrained variational analysis of optical spectra
• A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm
• Use of X-ray scattering functions in Kramers-Kronig analysis of reflectance
• Analytic continuation by averaging Padé approximants
• Analytical continuation of imaginary axis data for optical conductivity
• Spectral weight function for the half-filled Hubbard model: a singular value decomposition approach
• Superconducting fluctuations in a thin NbN film probed by the Hall effect
• Observation of quantum corrections to conductivity up to optical frequencies
• Optical models for thin layers

Cited by in corpus (1)

• Optical and transport properties of NbN thin films revisited