d+id Holographic Superconductors

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A holographic model of d+id superconductors based on the action proposed by Benini, Herzog, and Yarom [arXiv:1006.0731] is studied. This model has a charged spin two field in an AdS black hole spacetime. Working in the probe limit, the normalizable solution of the spin two field in the bulk gives rise to a d+id superconducting order parameter at the boundary of the AdS. We calculate the fermion spectral function in thissuperconducting background and confirm the existence of fermi arcs for non-vanishing Majorana couplings. By changing the relative strength γ of the d and id condensations, the position and the size of the fermi arcs are changed. When γ=1, the spectrum becomes isotropic and the spectral function is s-wave like. By changing the fermion mass, the fermi momentum is changed. We also calculate the conductivity for these holographic d+id superconductors where time reversal symmetry has been broken spontaneously. A non-vanishing Hall conductivity is obtained even without an external magnetic field.