The effects of an impurity with auxilary motion

When a light impurity is present in a lattice, the impurity may exhibit auxiliary motion to the lattice. We study the effects on the electronic spectrum and other properties of the material by the local oscillations of the impurity about its lattice equilibrium position (the impurity vibronic modes). These results are compared and contrasted for different electron couplings to the vibronic modes of the impurity, such as a Holstein-type coupling, where the vibronic modes modulate the on-site impurity energy, or a Peierls-type coupling, where the vibronic modes modulate the local hopping to the impurity.