Real Space Bogoliubov-de Gennes Equations Study of the Boson-Fermion Model

The boson-fermion model was proposed to describe superconductivity in short coherence length superconductors. In this work we use it to study impurity induced inhomogeneities in high temperature superconductors as found in numerous scanning tunnelling measurements. The model was formulated in real space and solved with help of Bogoliubov-de Gennes approach. Disorder in the boson or fermion subsystem is directly coupled to the superconducting order parameter and leads to severe changes of superconducting properties like local order parameter and density of states. We present the results for many impurities randomly distributed over otherwise clean and periodic two-dimensional square lattice.