Towards a holographic model of D-wave superconductors

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