 spectral anomalies: In hole-doped cases the same zero surface which causes the back-bending behavior around the antinode induces the incoherence around $(\pi,\pi)$, Fermi pockets and Fermi arcs, while a pile of pole and zero surfaces at a higher binding energy results in the high-energy kink (waterfall) and the incoherence around $(0,0)$. Moreover we have found a low-energy kink structure in the nodal dispersion. On the other hand, in electron-doped cases the zero surface which constitutes the pseudogap crosses the Fermi level around $(0,0)$, making electron pockets around the antinodes. All these features are consistent with experimental results. We would like to emphasize that the zero surface does not result from symmetry breakings, but is a direct consequence of the strong correlation effect, i.e., proximity to the Mott insulator.

To elucidate the effect of zeros at finite temperatures, we have also implemented CDMFT+CTQMC calculations. The results qualitatively agree with those of CDMFT+ED with a smearing factor $\eta$, which confirms that the thermal scatterings broaden the effect of zeros and indeed create the characteristic spectra similar to those observed in the cuprates.

To conclude, the origins of various anomalies in the electronic structure of the normal state in the high-$T_{\text{c}}$ cuprates are unified into the presence of the low-energy zero surface which persists against doping. The zero surface is also expected to cause anomalous metallic behaviors in other physical quantities, such as the specific heat, electronic resistivity, and Hall coefficient.[@ts99] Comparisons of these quantities with experiments remain for future studies.

Although the microscopic mechanism creating the zero surface has not been discussed in this paper, it has emerged clearly as the proximity to the Mott insulator. The similarity in the structure of the zero surfaces between the pseudogap and the Mott gap in the undoped system \[see Fig. 1(a) in Ref. \] also implies the Mott origin of the pseudogap. At the same