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The scanning tunneling microscopy experiments reveal nanoscale electronic inhomogeneities in Bi family of High Temperature Superconducting (HTSC) materials. In particular, modulations of the spectral gap in local density of states (LDOS) of order 100% on a scale of a few lattice constant lenghts were observed. Recently a positive correlation between these spatial modulations and position of dopant atoms were discovered. We study the spectral and thermodynamic properties of inhomogeneous d-wave superconductors described by a two component model (also called boson-fermion model). The model has been earlier proposed to describe some of the many features in high temperature superconductors. Here we assume that inhomogeneities originate from boson level disorder and take boson-fermion interaction in a form supporting d-wave symmetry of order parameter. Using real space Bogoliubov-de Gennes equations, we calculate fluctuations of order parameter, local density of states, Bogoliubov angle which is new spectroscopy measure, and specific heat. Our calculations reproduce observed correlations between magnitude of a gap and position of impurities and various aspects of LDOS, such as height of coherence peaks and broadening of the transition width. |
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