The problem of a polaron in quantum dot is retrieved using a modified LLP approach. The modification is intended to interpolate between the strong- and the weak-coupling limits of the problem. The polaronic effect is found to be more important for small dot sizes.
The problem of a two-dimensional magnetopolaron is investigated on the basis of a variational theory consisting of an adiabatic polaronic wavefunction combined with a perturbative correction by which it is possible to interrelate the strong and weak coupling counterparts of the coupled electron-phonon system. It is seen that the theory conveniently reproduces the desirable asymptotic limits in the different regimes of the problem. Furthermore, it is suggested that a satisfying improvement should be achieved if one adopts a suitably modified coherent phonon state operator which takes into account the fractional admixture of whether the lattice deformation tends to cover the entire Landau orbit or the mean electron position.
Using a variational approach, the interaction of an extrinsic electron with the surface modes of a semi-infinite medium is studied under the effect of an external magnetic field. The approach is to be valid for all values of the electron-surface-phonon coupling. In addition to the ground state energy, the number of phonons around the electron, and the spatial localization of the electron perpendicular and parallel to the surface are studied. It is observed that the magnetic field enhances the effective electron-phonon coupling and thus leads to an increased degree of localization of the electron toward the surface.
The problem of a polaronic donor in a strictly two-dimensional quantum well is studied using the variational approach. The approach covers the overall range of the electron-phonon coupling and the Coulomb binding strengths. The energy, the number of phonons around the electron, and the size of the polaron are calculated for the ground, and for the first two excited states. It is observed that the polaronic effects become more pronounced for strong Coulomb fields. The size of the polaron is found to be mainly dependent on the polaronic field, as the Coulomb field becomes weak.
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