  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.
