Stability of an Electron in Deformable Lattice –Force Range, Dimensionality and Potential Barrier–

Abstract

Local and global stabilities of an electron in deformable lattice with dimensionality δ and force range index λ are studied within the adiabatic approximation. Depending on the sign of the stability index: σ=δ-2λ-2, one finds the free state to be locally stable (σ>0) ith discontinuous transition to globally stable self-trapped state beyond a critical value of coupling constant g , to be marginal (σ=0) with local (as well as global) stability being governed by g , or to be locally instabilized (σ <0) towards the optimum lattice distortion which grows continuously from zero with increasing g . A phase diagram is presented for an electron interacting simultaneously with two types of phonon fields with \(\sigma \lessgtr 0\). The potential barrier for self-trapping of a Wannier exciton is studied with particular attention to the effect of its internal motion, and is compared with the observation.