| The long-range hoppings termed t' and t'' induces electron-hole asymmetry in the electronic states of cuprate superconductors. We first examine the single-particle spectral function A(k,w) by using the t-t'-t''-J model. The zero-temperature A(k,w) is numerically calculated for small clusters. Along the nodal direction quasiparticle bands in the hole-doped system are gapless, while in electron doping the bands are gapped up to optimum doping. A(k,w) around the antinodal region shows a gap-like feature appears in hole doping but not in electron doping, leading to a Fermi-arc behavior only in hole-doped system. Using the exact Green's functions A(k,w) of the t-t'-t''-J model, we construct the dynamical spin response function S(q,w) and the optical conductivity s(w). In the hole-doped system, S(q,w) shows an incommensurate structure, although a sandglass-like behavior observed in neutron scattering is unclear. The s(w) shows a good agreement with exact one of the t-t'-t''-J model, indicating small vertex corrections in the hole-doped system. On the contrary, S(q,w) and s(w) constructed in the electron-doped system disagree with the exact ones if antiferromagnetic correlation is strong. |
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