The optimally doped and underdoped region of the $t-J$ model at large N (N isthe number of spin components) is governed by the competition of d-wavesuperconductivity (SC) and a d Charge-Density Wave (d-CDW).The partialdestruction of the Fermi surface by the d-CDW and the resulting density ofstates are discussed. Furthermore, c-axis conductances for incoherent andcoherent tunneling are calculated, considering both an isotropic and ananisotropic in-plane momentum dependence of the hopping matrix element betweenthe planes. The influence of self-energy effects on the conductances is alsoconsidered using a model where the electrons interact with a dispersionless,low-lying branch of bosons. We show that available tunneling spectra frombreak-junctions are best explained by assuming that they result from incoherenttunneling with a strongly anisotropic hopping matrix element of the formsuggested by band structure calculations. The conductance spectra are thencharacterized by one single peak which evolves continuously from thesuperconducting to the d-CDW state with decreasing doping. The intrinsic c-axistunneling spectra are, on the other hand, best explained by coherent tunneling.Calculated spectra show at low temperatures two peaks due to SC and d-CDW. Withincreasing temperature the BCS-like peak moves to zero voltage and vanishes atT$_c$,exactly as in experiment.Our results thus can explain why break junctionand intrinsic tunneling spectra are different from each other. Moreover, theysupport a scenario of two competing order parameters in the underdoped regionof high-T$_c$ superconductors.
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