Self-trapping in quasi-one-dimensional solids

Electronic excitations in highly anisotropic quasi-one-dimensional solids are often regarded as being in a one-dimensional system. Here we determine the degree of anisotropy that is required to justify treating an excess carrier in this manner. In particular, we consider the adiabatic ground-state eigenfunctions for an excess electron in an electronically anisotropic solid in which the electron-lattice interaction is short ranged. In this circumstance an excess carrier in a one-dimensional system always self-traps to form a finite-radius (generally, large) polaron. On the other hand, in a three-dimensional system, an excess carrier will either self-trap to form a severely localized (small) polaron or it will not self-trap at all. We determine that the one-dimensional behavior typically requires the ratio of the electronic transfer integral for the easy direction to that for the transverse directions to be at least two orders of magnitude. Thus, estimated electronic anisotropies in many quasi-one-dimensional systems are not sufficient for these systems to be regarded as one dimensional with regard to self-trapping.