We study the influence of diagonal disorder (random site energy) of local pair (LP) site energies on the superconducting properties of a system of coexisting local pairs and itinerant electrons described by the (hard-core) boson-fermion model. Our analysis shows that the properties of such a model with s-wave pairing can be very strongly affected by the diagonal disorder in LP subsystem (the randomness of the LP site energies). This is in contrast with the conventional s-wave BCS superconductors, which according to the Andersons theorem are rather insensitive to the diagonal disorder (i.e. to nonmagnetic impurities). It has been found that the disorder effects depend in a crucial way on the total particle concentration n and the LP level position DELTA_o and depending on the parameters the system can exhibit various types of superconducting behaviour, including the LP-like, intermediate (MIXED)and the BCS-like. In the extended range of {n,DELTA_o} the superconducting ordering is suppressed by the randomness of the LP site energies and the increasing disorder induces a changeover from the MIXEDlike behaviour to the BCS-like one, connected with abrupt reduction of T_c and energy gap to zero. However, there also exist a definite range of {n,DELTA_o} in which the increasing disorder has a quite different effect: namely it can substantially enhance T_c or even lead to the phenomenon which can be called disorder induced superconductivity. Another interesting effect is a possibility of a disorder induced bound pair formation of itinerant electrons, connected with the change-over to the LP-like regime.
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