Stationary and dynamical properties of polarons in the anharmonic Holstein model

We study the semiclassical Holstein model with a hard nonlinear on-site potential in one, two, and three dimensions. Using stationary solutions, we obtain the ground-state phase diagram as a function of the parameter characterizing the nonlinearity as well as the electron-phonon coupling. The basic result is that in the presence of the nonlinear on-site potential medium and large polaron formation is also possible in two and three dimensions. Linearizing the equations of motion around the stationary solution, we calculate the normal modes and study their stability. Normal mode analysis shows the existence of a low-frequency pinning mode not only in one dimension (1D) but also in 2D and 3D. This result enables us to construct numerically one- and two-dimensional moving polarons and study their mobility properties. The dramatic reduction of the polaron effective mass is the most characteristic effect of the lattice nonlinearity.