Coulomb disorder effects on angle-resolved photoemission and nuclear quadrupole resonance spectra in cuprates

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 percent is sufficient to explain the line broadening observed in ${\text{Sr}}_2{\text{CuO}}_2{\text{Cl}}_2$, ${\text{La}}_2{\text{CuO}}_4$, and ${\text{Ca}}_2{\text{CuO}}_2{\text{Cl}}_2$. 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 line-shape 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) line shapes 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 ${\text{CuO}}_2$ layer the value of the gap is on the order of 10 meV while in the bulk it is reduced to the value about a few meV.