Abstract
Polaron states in cylindrical and spherical quantum dots with parabolic con-nement potentials are investigated applying the Feynman variational prin-ciple. It is observed that for both kinds of quantum dots the polaron energyand mass increase with the increase of Frohlich¤ electron-phonon couplingconstant and connement frequency. In the case of a spherical quantumdot, the polaron energy for the strong coupling is found to be greater thanthat of a cylindrical quantum dot. The energy and mass are found to bemonotonically increasing functions of the coupling constant and the con-nement frequency.
Highlights
Recent advances in the technology of fabrication of quasi-2D, -1D, -0D nanocrystals have stimulated the theoreticians’ interest in formulating models describing physical phenomena associated with nanocrystals [1,2,3,4,5,6,7,8,9,10,11,12]
Polaron energy is evaluated in [13,14,15] using perturbation theory, in [16] using the weak coupling approximation, in [17] using the dielectric continuum model and in [18] using the Feynman variational principle
Feynman polaron in a cylindrical quantum dot Consider the motion of an electron in a cylindrical quantum dot with a symmetric parabolic confinement potential
Summary
Polaron states in cylindrical and spherical quantum dots with parabolic confinement potentials are investigated applying the Feynman variational principle. It is observed that for both kinds of quantum dots the polaron energy and mass increase with the increase of Frohlich electron-phonon coupling constant and confinement frequency. In the case of a spherical quantum dot, the polaron energy for the strong coupling is found to be greater than that of a cylindrical quantum dot. The energy and mass are found to be monotonically increasing functions of the coupling constant and the confinement frequency.
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