An Anderson Impurity in a Semiconductor
We study an Anderson impurity in a semiconducting host using the density matrix renormalization group technique. We use the $U=0$ one--dimensional Anderson Hamiltonian at half filling as the semiconducting host since it has a hybridization gap. By varying the hybridization of the host, we can control the size of the semiconducting gap. We consider chains with 25 sites and we place the Anderson impurity (with $U>0$) in the middle of the chain. We dope the half--filled system with one hole and we find two regimes: when the hybridization of the impurity is small, the hole density and the spin are localized near the impurity. When the hybridization of the impurity is large, the hole and spin density are spread over the lattice. Additional holes avoid the impurity and are extended throughout the lattice. Away from half--filling, the semiconductor with an impurity is analogous to a double well potential with a very high barrier. We also examine the chemical potential as a function of electron filling, and we find that the impurity introduces midgap states when the impurity hybridization is small.