The role of Coulomb disorder, either of extrinsic origin or introduced by dopant ions in undoped and lightly-doped cuprates, is studied. We demonstrate that charged surface defects in an insulator lead to a Gaussian broadening of the Angle-Resolved Photoemisson Spectroscopy (ARPES) lines. The effect is due to the long-range nature of the Coulomb interaction. A tiny surface concentration of defects about a fraction of one per cent is sufficient to explain the line broadening observed in Sr$_2$CuO$_2$Cl$_2$, La$_2$CuO$_{4}$, and Ca$_{2}$CuO$_{2}$Cl$_{2}$. Due to the Coulomb screening, the ARPES spectra evolve dramatically with doping, changing their shape from a broad Gaussian form to narrow Lorentzian ones. To understand the screening mechanism and the lineshape evolution in detail, we perform Hartree-Fock simulations with random positions of surface defects and dopant ions. To check validity of the model we calculate the Nuclear Quadrupole Resonance (NQR) lineshapes as a function of doping and reproduce the experimentally observed NQR spectra. Our study also indicates opening of a substantial Coulomb gap at the chemical potential. For a surface CuO$_2$ layer the value of the gap is of the order of 10 meV while in the bulk it is reduced to the value about a few meV.
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