Holographic Josephson junction from massive gravity

We study the holographic superconductor-normal metal-superconductor (SNS) Josephson junction in de Rham-Gabadadze-Tolley massive gravity. If the boundary theory is independent of spatial directions, i.e., if the chemical potential is homogeneous in spatial directions, we find that the graviton mass parameter will make it more difficult for the normal metal-superconductor phase transition to take place. In the holographic model of the Josephson junction, it is found that the maximal tunneling current will decrease according to the graviton mass parameter. Besides, the coherence length of the junction decreases as well with respect to the graviton mass parameter. If one interprets the graviton mass parameter as the effect of momentum dissipation in the boundary field theory, this indicates that the stronger the momentum dissipation is, the smaller the coherence length is.