THE PHASE-DIAGRAM OF THE TIGHT-BINDING FROHLICH POLARON

We consider the ground-state energy of a tight-binding polaron in a po lar crystal. This system is represented by the Frohlich Hamiltonian in which the effective-mass kinetic term is replaced by the kinetic ener gy of an electron in the lattice potential. Also, a Debye cut-off is m ade on the phonon wavevectors. We write this Hamiltonian in a tight-bi nding representation and evaluate an upper bound to its ground-state e nergy 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 stro ng-coupling band state and a self-trapped state. The existence of thes e states depends on the value of two parameters: the electron-phonon c oupling strength and the electronic bandwidth. We also evaluate the li mits of validity of the continuum approximation for crystals of finite bandwidth by evaluating explicitly the corrections to the continuum a pproximation. We conclude that for small electron-phonon coupling (alp ha < 2.7) the continuum approximation is very good, that the strong-co upling band state does not exist in real crystals and that the self-tr apped state can be found in narrow-band polar materials.