The phase diagram of the tight-binding Frohlich polaron

Abstract

We consider the ground-state energy of a tight-binding polaron in a polar crystal. This system is represented by the Frohlich Hamiltonian in which the effective-mass kinetic term is replaced by the kinetic energy of an electron in the lattice potential. Also, a Debye cut-off is made on the phonon wavevectors. We write this Hamiltonian in a tight-binding representation and evaluate an upper bound to its ground-state energy using the Fock approximation of Matz and Burkey. This treatment is valid for any coupling strength and any degree of adiabaticity. We find three possible configurations: a weak-coupling band state, a strong-coupling band state and a self-trapped state. The existence of these states depends on the value of two parameters: the electron-phonon coupling strength and the electronic bandwidth. We also evaluate the limits of validity of the continuum approximation for crystals of finite bandwidth by evaluating explicitly the corrections to the continuum approximation. We conclude that for small electron-phonon coupling ( alpha <2.7) the continuum approximation is very good, that the strong-coupling band state does not exist in real crystals and that the self-trapped state can be found in narrow-band polar materials.