Towards A Holographic Model of D-Wave Superconductors

TL;DR

This paper extends the holographic superconductor model to D-wave symmetry, demonstrating a second-order phase transition with specific conductivity properties in a gravitational framework.

Contribution

It introduces a holographic D-wave superconductor model using a tensor field in AdS space, generalizing previous S-wave models.

Findings

D-wave condensate leads to a second-order phase transition with beta=1/2

AC conductivity is isotropic below T_c

No hard gap observed in the superconducting phase

Abstract

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+1 dimensional gravitational theory consists a symmetric, traceless second-rank tensor field and a U(1) gauge field in the background of the AdS black hole. Below T_c 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 beta = 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.