Abstract
The static and dynamical properties of an acoustic polaron in a two-dimensional electron-lattice system is studied numerically on the basis of Su, Schrieffer and Heeger's Hamiltonian (SSH Hamiltonian) extended to two dimensions. As for the static structure of the polaron, the coupling constant dependence of the width is analyzed. It is confirmed that, in contrast to the one-dimensional case, the two-dimensional acoustic polaron is stable only when the dimensionless electron-lattice coupling constant exceeds a certain critical value. As the coupling constant is reduced from a larger value, the polaron width increases, but the polaron becomes unstable before the width diverges. The dynamics of the polaron is studied by applying an external electric field which accelerate the polaron in a natural way. Similarly to the one-dimensional system the polaron velocity shows a saturation, though the saturation velocity is about one quarter of that in the one-dimensional case which is known to be nearly equal to the sound velocity of the system. From the relation between the velocity and the energy of the polaron the effective mass is estimated.
