  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 this\ superconducting background and
confirm the existence of fermi arcs for non-vanishing Majorana couplings. By
changing the relative strength $\gamma $ of the $d$ and $id$ condensations, the
position and the size of the fermi arcs are changed. When $\gamma =1$, 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.
