Competition between superconductivity and the pseudogap phase in the t-J model

The t-J model in the large N limit (N denotes the number of spin components) yields a pseudogap phase in the underdoped region which is related to a d-wave charge density wave (d-CDW). We present results for the doping dependence of the superconducting and d-CDW order parameters as well as for collective excitations in the presence of these two order parameters. We argue that the electronic Raman spectrum with B$_{1g}$ symmetry probes the amplitude fluctuations of the d-CDW at zero momentum.