Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors

Details Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors

2009-07-22

arxiv.org/abs/0907.3775v3

J. Phys. A 43:145304, 2010

Physics

Condensed Matter

Superconductivity

20 pages, 7 figures, calculation of Casimir energy added

Scientific paper

10.1088/1751-8113/43/14/145304

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.

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