Effect of local potential variations in the model of hole superconductivity

Physica C 194, 119 (1992).

In the model of hole superconductivity the strength of the pairing interaction depends on the local carrier density. This gives rise to a dependence of the gap function $\Delta_k$ on the band energy $\epsilon_k$. Fluctuations in the local potential energy will result in different values of $\Delta_k$ at the Fermi energy and hence in different values of the local energy gap. In particular, the energy gap can be sharply reduced. We study this behavior by numerical solution of the Bogoliubov-de Gennes equations for the model. The behavior is contrasted with what occurs in the attractive Hubbard model, where local potential fluctuations have negligible effect. The physical origin of this behavior and the possible relevance to high $T_c$ oxides is discussed.