Evolution of the in-gap state in high-T_c cuprates

An exact diagonalization technique on small lattices is used to calculate the single-particle spectral function A(k,ω) for one- and three-band Hubbard models at various parameter values and doping rates, thereby examining the low-energy electronic structure (or in-gap state) of the doped CuO₂ plane in high-T_c superconducting cuprates. It is illustrated that, by carrier doping, the dispersive state of the charge excitation gap at half filling undergoes a strongly momentum-dependent spectral-weight transfer, and evolves into the new state with a free-electron-like dispersion that forms the in-gap state characteristic of a large Fermi surface consistent with Luttinger’s sum rule. The quasiparticlelike band narrowing observed is shown to depend sensitively on the parameter values and doping rate.