  One of the most intriguing puzzle is why there is a coexistence of Fermi arcs
and Fermi pockets in the pseudogap phase of cuprate superconductors? This
puzzle is calling for an explanation. Based on the t-J model in the
fermion-spin representation, the coexistence of the Fermi arcs and Fermi
pockets in cuprate superconductors is studied by taking into account the
pseudogap effect. It is shown that the pseudogap induces an energy band
splitting, and then the poles of the electron Green's function at zero energy
form two contours in momentum space, however, the electron spectral weight on
these two contours around the antinodal region is gapped out by the pseudogap,
leaving behind the low-energy electron spectral weight only located at the
disconnected segments around the nodal region. In particular, the tips of these
disconnected segments converge on the hot spots to form the closed Fermi
pockets, generating a coexistence of the Fermi arcs and Fermi pockets.
Moreover, the single-particle coherent weight is directly related to the
pseudogap, and grows linearly with doping. The calculated result of the overall
dispersion of the electron excitations is in qualitative agreement with the
experimental data. The theory also predicts that the pseudogap-induced
peak-dip-hump structure in the electron spectrum is absent from the hot-spot
directions.
