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The Chiral d-density wave (CDDW) order, at the anti-ferromagnetic wave vector(pi,pi), is assumed to represent the pseudo-gap (PG) state of a hole-dopedcuprate superconductor. The pairing interaction required for the PG phasecorresponds to a repulsive interaction of Coulombic origin. The d-wavesuperconductivity (DSC), driven by an appropriate assumed attractiveinteraction, is discussed within the mean-field framework together with theCDDW ordering. The single-particle excitation spectrum in the CDDW and DSCstate is characterized by the Bogolubov quasi-particle bands-a characteristicfeature of SC state. The coupled gap equations are solved self-consistentlytogether with the equation to determine the chemical potential. With thepinning of the van Hove-singularities close to the chemical potential, one isable to calculate the thermodynamic and transport properties of the under-dopedcuprates in a consistent manner. The electronic specific heat displaysnon-Fermi liquid feature in the CDDW state. The CDDW and DSC are found torepresent two competing orders as the former brings about a depletion of thespectral weight (and Raman response function density) available for pairing inthe anti-nodal region of momentum space.This is not in agreement with apreformed pairing scenario and justifies the different structures we haveassumed for the pseudo-gap and the superconducting gap. Furthermore, these gapsin the excitation spectrum do not merge into a single quadrature gap. It isalso shown that the depletion of the spectral weight below Tc at energieslarger than the gap amplitude occurs. This is an indication of thestrong-coupling superconductivity in cuprates. The calculation of the ratio ofthe quasi-particle thermal conductivity and temperature in the superconductiongphase is found to be constant in the limit of near-zero quasi-particlescattering rate.Comment: 17 pages, 8 figures. arXiv admin note: substantial text overlap with  arXiv:1111.0928. This article is withdrawn due to a preexisting version  onlin

ON d+id DENSITY WAVE AND SUPERCONDUCTING ORDERINGS IN HOLE-DOPED CUPRATES