  Motivated by recent developments in the experimental study of Bose-Fermi
mixtures, we investigate ground-state phase diagrams and excitation spectra for
Bose-Fermi mixtures in a three-dimensional (3D) optical lattice. The Gutzwiller
approximation is used to identify a new phase in which both superfluid bosons
and metal fermions coexist. As a useful probe to identify the quantum phases,
we also calculate the excitation spectra. In Mott insulator phase, two
excitation features appear in the spectra that correspond to particle and hole
excitations. In superfluid phase, there are Bogoliubov modes and amplitude
modes. In coexisting phase, two gapless dispersive modes are identified, which
shift due to interaction between bosons and fermions.
