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The boson-fermion (BF) model has been proposed to describe superconductivityin short coherence length superconductors. In this work we use it to studyimpurity induced inhomogeneities in high temperature superconductors (HTS) asfound in numerous scanning tunnelling measurements. The model has beenformulated in real space and solved with help of Bogolubov-de Gennes approach.Disorder in the boson or fermion subsystem is directly coupled to thesuperconducting order parameter and leads to severe changes of superconductingproperties like local order parameter and density of states. We present theresults for many impurities randomly distributed over otherwise clean andperiodic two-dimensional square lattice.

Real space Bogolubov-de Gennes equations study of the boson-fermion model