Recent atomic resolution scanning tunneling microscope (STM) measurements discovered remarkable electronic inhomogeneity, i.e., nanoscale spatial variations of the local density of states (LDOS) and the superconducting energy gap, in the high-$T_c$ superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+x}.$ Based on the experimental findings, we conjectured that the inhomogeneity arises from variations in local oxygen doping level and may be generic of doped Mott insulators. In this paper, we provide theoretical support for this picture. We study a doped Mott insulator within a generalized t-J model, where doping is accompanied by ionic Coulomb potentials centered in the BiO plane located a distance $d_s$ away from the ${\mathrm{CuO}}_2$ plane. We solve, at the mean-field level, a set of spatially unrestricted Bogoliubov–de Gennes equations self-consistently to obtain the distributions of the hole concentration, the valence bond, and the pairing order parameters for different nominal/average doping concentrations. We calculate the LDOS spectrum, the integrated LDOS, and the local superconducting gap as those measured by STM, make detailed comparisons to experiments, and find remarkable agreement with the experimental data. We emphasize the unconventional screening of the ionic potential in a doped Mott insulator and show that nonlinear screening dominates on nanometer scales, comparable to the short coherence length of the superconductor, which is the origin of the electronic inhomogeneity. It leads to strong inhomogeneous redistribution of the local hole density and promotes the notion of local doping concentration (LDC). We find that the inhomogeneity structure manifests itself at all energy scales in the STM tunneling differential conductance, and elucidate the similarity and the differences between the data obtained in the constant tunneling current mode and the same data normalized to reflect constant tip-to-sample distance. We also discuss the underdoped case where nonlinear screening of the ionic potential turns the spatial electronic structure into a percolative mixture of patches with smaller pairing gaps embedded in a background with larger gaps to single particle excitations.

• Received 2 July 2001

DOI:https://doi.org/10.1103/PhysRevB.65.064509