We have studied a holographically dual description of superconductor in (2 + 1)-dimensions in the presence of applied magnetic field, and observed that there exists a critical value of magnetic field, below which a charged condensate can form via a second order phase transition.

The holographic model for S-wave high T c superconductors developed by Hartnoll, Herzog, and Horowitz is generalized to describe D-wave superconductors. The 3 þ 1 dimensional gravitational theory consists of a symmetric, traceless second-rank tensor field and a Uð1Þ gauge field in the background of the anti-de Sitter black hole. Below T c the tensor field, which carries the Uð1Þ charge, undergoes the Higgs mechanism and breaks the Uð1Þ symmetry of the boundary theory spontaneously. The phase transition characterized by the D-wave condensate is second order with the mean field critical exponent ¼ 1=2.As expected, the AC conductivity is isotropic below T c , and the system becomes superconducting in the DC limit but has no hard gap.

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