Effect of local electron-electron correlation in hydrogen-like impurities in Ge

We have studied the electronic and local magnetic structure of the hydrogen interstitial impurity at the tetrahedral site in diamond-structure Ge, using an empirical tight binding + dynamical mean field theory approach because within the local density approximation (LDA) Ge has no gap. We first establish that within LDA the 1s spectral density bifurcates due to entanglement with the four neighboring sp3 antibonding orbitals, providing an unanticipated richness of behavior in determining under what conditions a local moment hyperdeep donor or Anderson impurity will result, or on the other hand a gap state might appear. Using a supercell approach, we show that the spectrum, the occupation, and the local moment of the impurity state displays a strong dependence on the strength of the local on-site Coulomb interaction U, the H-Ge hopping amplitude, the depth of the bare 1s energy level epsilon_H, and we address to some extent the impurity concentration dependence. In the isolated impurity, strong interaction regime a local moment emerges over most of the parameter ranges indicating magnetic activity, and spectral density structure very near (or in) the gap suggests possible electrical activity in this regime.