  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-doped
cuprate superconductor. The pairing interaction required for the PG phase
corresponds to a repulsive interaction of Coulombic origin. The d-wave
superconductivity (DSC), driven by an appropriate assumed attractive
interaction, is discussed within the mean-field framework together with the
CDDW ordering. The single-particle excitation spectrum in the CDDW and DSC
state is characterized by the Bogolubov quasi-particle bands-a characteristic
feature of SC state. The coupled gap equations are solved self-consistently
together with the equation to determine the chemical potential. With the
pinning of the van Hove-singularities close to the chemical potential, one is
able to calculate the thermodynamic and transport properties of the under-doped
cuprates in a consistent manner. The electronic specific heat displays
non-Fermi liquid feature in the CDDW state. The CDDW and DSC are found to
represent two competing orders as the former brings about a depletion of the
spectral weight (and Raman response function density) available for pairing in
the anti-nodal region of momentum space.This is not in agreement with a
preformed pairing scenario and justifies the different structures we have
assumed for the pseudo-gap and the superconducting gap. Furthermore, these gaps
in the excitation spectrum do not merge into a single quadrature gap. It is
also shown that the depletion of the spectral weight below Tc at energies
larger than the gap amplitude occurs. This is an indication of the
strong-coupling superconductivity in cuprates. The calculation of the ratio of
the quasi-particle thermal conductivity and temperature in the superconductiong
phase is found to be constant in the limit of near-zero quasi-particle
scattering rate.
