Effect of a deformation potential coupling on the ground-state energy of a tight-binding Fröhlich polaron

Abstract

An upper bound to the ground-state energy of a tight-binding polaron (a polaron in a narrow band material) in a polar crystal is obtained, in the nonadiabatic limit, from a Hamiltonian that includes two contributions to the electron–phonon coupling: a short-range deformation potential interaction and a long-range dipolar interaction. A Debye cutoff on the phonon wave vectors is also assumed. A variational ground-state energy is deduced, using a modification of a tight-binding type Ansatz used in small-polaron theory, in the nonadiabatic limit. In the weak-coupling limit the ground state corresponds to that of a large polaron, while the strong-coupling limit gives a small-polaron state. The bandwidth greatly influences the state of the system and phase diagrams are presented that show the regions where the small and the large polarons are energetically favored. We find, in this variational context, that for a narrow band, the transition between the self-trapped state and the band state is continuous and that an intermediate-polaron state is involved. For a larger but moderate bandwidth, the system is found to switch abruptly from one state to the other, with a coexistence of both states around the transition region. Each of the two types of coupling is found to have an equivalent role in increasing the trapping energy of the electron and in reducing the bandwidth exponentially. Furthermore, their effect is cumulative.