  One of the central issues in the recent study of cuprate superconductors is
the interplay of charge order with superconductivity. Here the interplay of
charge order with superconductivity in cuprate superconductors is studied based
on the kinetic-energy-driven superconducting (SC) mechanism by taking into
account the intertwining between the pseudogap and SC gap. It is shown that the
appearance of the Fermi pockets is closely associated with the emergence of the
pseudogap. However, the distribution of the spectral weight of the SC-state
quasiparticle spectrum on the Fermi arc, or equivalently the front side of the
Fermi pocket, and back side of Fermi pocket is extremely anisotropic, where the
most part of the spectral weight is located around the tips of the Fermi arcs,
which in this case coincide with the hot spots on the electron Fermi surface
(EFS). In particular, as charge order in the normal-state, this EFS instability
drives charge order in the SC-state, with the charge-order wave vector that is
well consistent with the wave vector connecting the hot spots on the straight
Fermi arcs. Furthermore, this charge-order state is doping dependent, with the
charge-order wave vector that decreases in magnitude with the increase of
doping. Although there is a coexistence of charge order and superconductivity,
this charge order antagonizes superconductivity. The results from the SC-state
dynamical charge structure factor indicate the existence of a quantitative
connection between the low-energy electronic structure and collective response
of the electron density. The theory also shows that the pseudogap and charge
order have a root in common, they and superconductivity are a natural
consequence of the strong electron correlation.
