Polaron dynamics in a two-dimensional anharmonic Holstein model

A generalized two-dimensional semiclassical Holstein model with a realistic on-site potential that contains anharmonicity is studied. More precisely, the lattice subsystem of anharmonic on-site oscillators is supposed to have a restricting core. The core plays the role of an effective saturation nonlinearity for the polaron (self-trapped) solutions. We apply the “logarithmic” potential approximation which allows us to use effectively a variational approach, on one hand, and to study the realistic situation of the potential core and saturation nonlinearity, on the other hand. Analytical estimates suggest the existence of wide polarons, contrary to the case with harmonic on-site potential. Numerical simulations confirm these estimates and show stability of such polaron solutions. We develop a numerical technique which allows us to obtain the profile of extended moving polarons. Simulations show that these polarons can propagate for long distances on the plane retaining their shape and velocity. Collision effects of the two-dimensional polarons are also investigated.