Holographic conductivity of zero temperature superconductors

TL;DR

This paper calculates the holographic conductivity of zero temperature superconductors using a numerical model, confirming non-zero conductivity and discovering additional solutions with similar properties.

Contribution

It extends previous models by numerically analyzing conductivity at zero temperature and identifying new solutions that maintain non-zero conductivity.

Findings

Confirmed non-zero conductivity at zero temperature.

Found additional normalizable solutions with the same asymptotic behavior.

Validated the universal relation between conductivity and reflection coefficient.

Abstract

Using the recently found by G. Horowitz and M. Roberts (arXiv:0908.3677) numerical model of the ground state of holographic superconductors (at zero temperature), we calculate the conductivity for such models. The universal relation connecting conductivity with the reflection coefficient was used for finding the conductivity by the WKB approach. The dependence of the conductivity on the frequency and charge density is discussed. Numerical calculations confirm the general arguments of (arXiv:0908.3677) in favor of non-zero conductivity even at zero temperature. In addition to the Horowitz-Roberts solution we have found (probably infinite) set of extra solutions which are normalizable and reach the same correct RN-AdS asymptotic at spatial infinity. These extra solutions (which correspond to larger values of the grand canonical potential) lead to effective potentials that also vanish at the horizon and thus correspond to a non-zero conductivity at zero temperature.