Dimensional mismatch of the electron-phonon system and large polaron stability
We consider the scaling arguments in the adiabatic limit for materials in which one-dimensional (1D) electronic behavior is influenced by a higher-dimensional vibrational system. The system under consideration consists of a collection of widely separated parallel molecular chains, perfectly one dimensional in respect to their electronic characteristics, embedded in a three-dimensional (3D) lattice. We found that dimensional mismatch between electronic subsystem and lattice may seriously affect polaron stability. For the realistic systems with anisotropic phonon spectrum large polaron stability requires that polaron radius cannot exceed some critical value which is of the order of the interchain spacing. Finally, large polaron stability criterion is formulated in dependence of the values of the basic system parameters.