Superconductivity Induced by Negative Centers

We study the effect of random dilution of attraction centers on electron pairing in a generalization of the negative $U$ Hubbard model where the interaction $U_i$, defined on the two dimensional lattice, can be $-|U|$ and 0 with probability $c$ and $1-c$ depending on the lattice site $i$. Using the determinant quantum Monte Carlo approach, we find the critical concentration $c_0$ of negative centers which leads to superconductivity, and show how the evolution of the local density on the two types of sites lends insight into the formation of global phase coherence.