Influence of the atomic-scale inhomogeneity of the pair interaction on   extracted from the STM spectra characteristics of high-$T_c$ superconductors
  The influence of the atomic-scale inhomogeneities of the pairing interaction strength on the superconducting order parameter and the conductance spectra measurable by STM is studied in the framework of weak-coupling BCS-like theory for two-dimensional lattice model. First of all, it is found that the inhomogeneity having the form of atomic-scale regions of enhanced pair interaction increases the ratio of the local low-temperature gap in differential conductance spectra to the local temperature of vanishing the gap $2\Delta_g/T_p$. Even in the framework of mean-field treatment this ratio is shown to be larger than the one corresponding to the homogeneous case. It is shown that the effect of thermal phase fluctuations of the superconducting order parameter can further increase this ratio. Taking them into account in the framework of a toy model we obtained the ratio $2\Delta_g/T_p$ to be $\sim 7-8$. It is found that the additional atomic-scale hopping element disorder and weak potential scatterers, which can also take place in cuprate materials, have no considerable effect on the statistical properties of the system, including the distribution of the gaps, $T_p$ and the ratio $2\Delta_g/T_p$. The second consequence of the atomic-scale order parameter inhomogeneity is the anticorrelation between the low-temperature gap and the high-temperature zero-bias conductance. The obtained results could bear a relation to recent STM measurements. 
A. M. Bobkov, I. V. Bobkova