Normal-state pseudogap and electron flat dispersion in copper oxide materials

The anomalous momentum and doping dependence of the electron spectral function and electron dispersion for copper oxide materials in the underdoped regime are studied within the t-J model. It is shown that the electron spectrum is changed with dopings, and the electron dispersion exhibits a flat band around ($\pi$,0) point in the Brillouin zone, which leads to the normal-state pseudogap formation. The theoretical results are consistent with the experiments and numerical simulations.