Negative refraction and superconductivity

We discuss exotic properties of charged hydrodynamical systems, in the broken superconducting phase, probed by electromagnetic waves. Motivated by general arguments from hydrodynamics, we observe that negative refraction, namely the propagation in opposite directions of the phase velocities and of the energy flux, is expected for low enough frequencies. We corroborate this general idea by analyzing a holographic superconductor in the AdS/CFT correspondence, where the response functions can be explicitly computed. We study the dual gravitational theory both in the probe and in the backreacted case. We find that, while in the first case the refractive index is positive at every frequency, in the second case there is negative refraction at low enough frequencies. This is in agreement with hydrodynamic considerations.