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Magnetic Properties of (Holographic) Superconductors

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I will discuss magnetic properties of superconductors, first in a model independent way and then by using holographic models. This approach has the advantage of highlighting the generic features of superconducting materials and, at the same time, the predictions of specific models. I will start with the Meissner effect and the vortices. Given the importance of the magnetic field dynamics in these phenomena, I will describe how to introduce a dynamical gauge field in holography. Then I will show that the holographic superconductor, like all known high-temperature superconductors, is Type II. Finally, I will discuss the case of hollow cylindrical superconductors threaded by an axial magnetic field. The physics of these systems is periodic with respect to the magnetic flux, with a period that depends on weather non-local quantum effects are suppressed or not. In the holographic model these effects are not suppressed when the radius of the cylinder is below the critical value at which the Hawking-Page phase transition takes place.