Self-Trapping and Drift Motion of an Electron

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Abstract
The importance of the acoustical mode lattice vibration for self‐trapping of an electron is emphasized in this paper. It is shown that when the coupling constant between the electron and the acoustical vibration exceeds a certain critical value, the effective mass of the electron changes discontinuously to such an enormous value that it is practically allowed to take a localized self‐trapping state as an eigenstate, in contrast to the case of polar mode, in which the effective mass changes continuously with coupling constant. This difference is attributed to the different force range of the electron‐lattice interaction in the two cases. The self‐trapping state as well as the activated state for the hopping motion are discussed within the framework of adiabatic approximation by making use of Koster‐Slater's method. It is pointed out that drift motion is more probable than the hopping motion for the intermediate magnitude of coupling constant.

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