MAGNETOPOLARON IN A CYLINDRICAL QUANTUM DOT

Abstract

We examine the magnetopolaron state in a cylindrical quantum dot with a transverse parabolic potential and a high rectangular potential well in the longitudinal direction. The quadratic dependence of the magnetopolaron energy versus Fröhlich electron–phonon coupling constant for different cyclotron radii and constant structure radius is modulated by a logarithmic function seems to depend on the Fröhlich coupling constant. The same law is seen in the case of magnetopolaron energy versus Fröhlich electron–phonon coupling constant for different structure radii and constant cyclotron radius. The energies are seen to be lifted in different fashions in the case of the structure and cyclotron radii. The high degrees of confinement (or high magnetic field) lead to an enhancement in the effective electron–phonon coupling that in turn brings about the possibility that in spite of weak polar coupling as in GaAS say, the polaron problem may also have strong-coupling counterparts arising from confinement or magnetic field effects. The polaron mass increases with increasing Fröhlich electron–phonon coupling constant. The dependence seems to be fourth-order law of the Fröhlich coupling constant modulated by a logarithmic function.