| Self-trapped electrons is very important for to understand theoptical properties of materials, people have made a lot of research.the short-range interactions between the electrons and thephonons can be regarded as the trigger electronic trap.Therefore,we first need to get Hamiltonian for electron interactionwith longitudinal phonon, then issues related to research on theAcoustic Polaron self-trapping.We first obtained the new Hamiltonian for electron interactionwith longitudinal phonon in three-dimensional system, compare theresult with peeters’. Proving the applicability of the new method todeduce system Hamiltonian.Then research the two-dimensional Acoustic Polaron self-trappingproblems. Use the method that the electronic and the phononthrough deformation potential coupling to derived two-dimensionalHamiltonian about electron and longitudinal phonon interction. Andthen use Huybrechts variational methed to calculate theground-state energy. We found our results same with Farias’. It isnot consistent with the general law of Acoustic Polaron self-trapping. Therefore, in the derivation process of theground-state energy, considering the real meaning planar materialsis not exist in nature. The2D that we talkabout is just onedimension is bound and the other two dimensions are free on thebasis of3D similar to the two-dimensional. We join bγ in the finalintegration, so that our derivation is more close to the actual. Usethe result to draw the change curve that ground-state energy of theAcoustic Polaron along with the electron-phonon coupling constant,and then discussed to make concluded. Use the same methed tofuture study the problems about one-dimension Acoustic Polaronself-trapping.Comparison of3D,2D,1D Acoustic Polaron self-trappingcondition, can be seen: the Acoustic Polaron each dimension has itstrap criterion. dimension is low, Acoustic Polaron self-trapping moreeasily. This is helpful for us to judge some Acoustic Polaronself-trapping problem of the actual material in theory. |
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