  Considering the effects of charge screening, we propose a new numerical
recipe within the framework of Thomas-Fermi approximation, where the properties
of nuclear matter throughout a vast density range can be obtained
self-consistently. Assuming spherical and cylindrical approximations for the
Wigner-Seitz cell, typical nuclear matter structures (droplet, rod, slab, tube,
bubble, and uniform) are observed. We then investigate the EOSs and microscopic
structures of nuclear matter with both fixed proton fractions and
$\beta$-equilibration, where two covariant density functionals DD-LZ1 and
DD-ME2 are adopted. Despite the smaller slope $L$ of symmetry energy obtained
with the functional DD-LZ1, the curvature parameter $K_\mathrm{sym}$ is much
larger than that of DD-ME2, which is attributed to the peculiar
density-dependent behavior of meson-nucleon couplings guided by the restoration
of pseudo-spin symmetry around the Fermi levels in finite nuclei. Consequently,
different mass-radius relations of neutron stars are predicted by the two
functionals. Different microscopic structures of nonuniform nuclear matter are
obtained as well, which are expected to affect various physical processes in
neutron star properties and evolutions.
