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The recently discovered charge order is an intrinsic and universal property of cuprate superconductors, however, its microscopic origin remains debated. Here we review briefly the theoretical work about the nature of charge order in cuprate superconductors. In particular, we show that the electron self-energy obliterates the electron Fermi surface around the antinodal region, leaving behind disconnected Fermi arcs located around the nodal region. The charge-order state on the other hand is driven by the Fermi-arc instability, with a characteristic wavevector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Since the pseudogap emanates from the electron self-energy, the Fermi arc, charge order, and pseudogap in cuprate superconductors are intimately related each other. [ABSTRACT FROM AUTHOR]

The recently discovered charge order is a generic feature of cuprate superconductors, however, its microscopic origin remains debated. Within the framework of the fermion-spin theory, the nature of charge order in the pseudogap phase and its evolution with doping are studied by taking into account the electron self-energy (then the pseudogap) effect. It is shown that the antinodal region of the electron Fermi surface is suppressed by the electron self-energy, and then the low-energy electron excitations occupy the disconnected Fermi arcs located around the nodal region. In particular, the charge order state is driven by the Fermi-arc instability, with a characteristic wave vector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Moreover, although the Fermi arc increases its length as a function of doping, the charge order wave vector reduces almost linearity with the increase of doping. The theory also indicates that the Fermi arc, charge order and pseudogap in cuprate superconductors are intimately related to each other, and all of them emanates from the electron self-energy due to the interaction between electrons by the exchange of spin excitations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]