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Holographic superconductors. (English) Zbl 1329.81390
Summary: It has been shown that a gravitational dual to a superconductor can be obtained by coupling anti-de Sitter gravity to a Maxwell field and charged scalar. We review our earlier analysis of this theory and extend it in two directions. First, we consider all values for the charge of the scalar field. Away from the large charge limit, backreaction on the spacetime metric is important. While the qualitative behaviour of the dual superconductor is found to be similar for all charges, in the limit of arbitrarily small charge a new type of black hole instability is found. We go on to add a perpendicular magnetic field $$B$$ and obtain the London equation and magnetic penetration depth. We show that these holographic superconductors are Type II, i.e., starting in a normal phase at large $$B$$ and low temperatures, they develop superconducting droplets as $$B$$ is reduced.

##### MSC:
 81V17 Gravitational interaction in quantum theory 82D55 Statistical mechanics of superconductors 81T20 Quantum field theory on curved space or space-time backgrounds
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