The Ginzburg-Landau Theory of a Holographic Superconductor
Abstract
The general Ginzburg-Landau formulation of a holographic superconductor is developed near the transition temperature in the probe limit for two kinds of conformal dimension. Below the transition temperature, T<Tc, the order-parameter scales with 1-TTc as expected. The G-L free energy in grand caonnical ensemble and canonical ensemble are derived and the gradient term is studied. Furthermore this scaling coefficient of order-parameter takes different values in the grand canonical ensemble and the canonical ensemble, suggesting the strong coupling nature of the boundary field theory of the superconductiviy.
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