Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors

TL;DR

This paper introduces an efficient method for calculating the optical and AC conductivity of superconductors at complex frequencies, facilitating thermodynamic and dispersion energy computations with improved speed, especially at imaginary frequencies.

Contribution

It provides a novel analytic continuation formula for superconductor conductivity applicable to arbitrary complex frequencies, enhancing computational efficiency over previous methods.

Findings

Faster evaluation of conductivity at imaginary frequencies.

Simplified low-frequency conductivity expansion.

Accurate calculation of Casimir free energy in superconducting cavities.

Abstract

We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and AC conductivity of a homogeneous superconductor with arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers--Kronig transforms. A number of applications illustrates its efficiency: a simplified low-frequency expansion of the conductivity, the electromagnetic bulk self-energy due to longitudinal plasma oscillations, and the Casimir free energy of a superconducting cavity.