No abstract

It is very interesting that all holographic superconductors, such as s-wave, p-wave and d-wave holographic superconductors, show the universal mean-field critical exponent 1/2 at the critical temperature, just like Gindzburg-Landau (G-L) theory for second order phase transitions. Now it is believed that the universal critical exponents appear because the dual gravity theory is classic in the large N limit. However, even in the large N limit there is an exception called "non-mean-field theory": an extension of

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.

The p-wave and p + ip-wave holographic superconductors with fixed DC supercurrent are studied by introducing a non-vanishing vector potential. We find that close to the critical temperature T c of zero current, the numerical results of both the p wave model and the p + ip model are the same as those of Ginzburg-Landau (G-L) theory, for example, the critical current j c ∼ (T c − T ) 3/2 and the phase transition in the presence of a DC current is a first order transition. Besides the similar results between both models, the p + ip superconductor shows isotropic behavior for the supercurrent, while the p-wave superconductor shows anisotropic behavior for the supercurrent.

In this paper, we investigate the p+ip superfluid phases in the complex vector field holographic p-wave model. We find that in the probe limit, the p+ip phase and the p-wave phase are equally stable, hence the p and ip orders can be mixed with an arbitrary ratio to form more general p+λip phases, which are also equally stable with the p-wave and p+ip phases. As a result, the system possesses a degenerate thermal state in the superfluid region. We further study the case on considering the back-reaction on the metric, and we find that the degenerate ground states will be separated into pwave and p+ip phases, and the p-wave phase is more stable. Finally, due to the different critical temperature of the zeroth order phase transitions from p-wave and p+ip phases to the normal phase, there is a temperature region where the p+ip phase exists but the p-wave phase does not. In this region we find the stable holographic p+ip phase for the first time.