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

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

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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) with 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 σ\lessgtr0. 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.

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