Holographic superconductors at low temperatures

Holographic models of superconductivity offer a promising approach to the understanding of strongly coupled superconductors. Their properties are derived from non-linear field equations which are hard to solve, especially at low temperatures. I will discuss analytic tools that generate solutions down to zero temperature. This exploration is important for the understanding of the ground state of these systems. I will present results in the probe limit (vanishing chemical potential $\mu$), as well as the extremal limit (small critical temperature to chemical potential ($T_c/\mu$) ratio).