Real space Bogolubov-de Gennes equations study of the boson-fermion   model
  The boson-fermion (BF) model has been proposed to describe superconductivity in short coherence length superconductors. In this work we use it to study impurity induced inhomogeneities in high temperature superconductors (HTS) as found in numerous scanning tunnelling measurements. The model has been formulated in real space and solved with help of Bogolubov-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. 
Jaromir Krzyszczak, Tadeusz Doma\'nski, Karol I. Wysoki\'nski