Interaction of electrons with acoustic phonons via the deformation potential in one dimension

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Abstract
We investigate the one-dimensional polaron in the case where the electron couples to the acoustic phonons via the deformation potential. In addition to the fact that this model may apply for some quasi-one-dimensional systems, it has several interesting features. The model exhibits the same type of divergence as the piezoelectric polaron but in a mathematically more tractable form. Realistic values of the deformation potential suggest that strong coupling applies. We show that in the strong-coupling limit the theory reduces to another polaron model that Gross has shown to be exactly solvable. We also obtain a soliton-like model for the moving polaron. The first correction to the strong-coupling limit has an ultraviolet divergence which is caused by the fact that the short-wavelength phonons follow the motion of the electron in its self-trapped state. This situation is also analogous to the piezoelectric polaron.