Bound polaron in a narrow-band polar crystal

Abstract

The ground-state energy of a bound polaron in a narrow-band polar crystal (such as a metal oxide) is studied using variational wave functions. We use a Fröhlich-type Hamiltonian on which the effective mass approximation has not been effected and in which a Debye cutoff is made on the phonon wave vectors. The wave functions that are used are general enough to allow the existence of a band state and of a self-trapped state and are reliable in the nonadiabatic limit. We find that three ground states are possible for this system. First, for small electron–phonon coupling, moderate bandwidth, and shallow impurities, the usual effective-mass hydrogenic ground state is found. For a narrow bandwidth and a deep defect, a collapsed state is predicted in which the polaron coincides with the position of the defect. Finally, for moderate electron–phonon coupling, narrow bandwidth, and a very weak defect, a self-trapped polaron in a hydrogenic state is predicted. Our conclusions are presented as asymptotic expansions and as phase diagrams indicating the values of the parameters for which each phase can be found.