Energy levels of two- and three-dimensional polarons in a magnetic field

Abstract

The influence of the electron-phonon interaction on the Landau levels of two- (2D) and three-dimensional (3D) electrons are studied within second-order perturbation theory. It is found that polaron effects in ideal 2D systems are larger than in 3D systems which agrees with recent results of Das Sarma and Larsen. Analytical and numerical results are presented for the electron-phonon correction to the different Landau levels (n) below the LO-phonon continuum. Special attention is paid to the small and large magnetic-field limit and to the splitting of the Landau levels which occurs at n${\ensuremath{\omega}}_{c}$\ensuremath{\approxeq}${\ensuremath{\omega}}_{0}$ (${\ensuremath{\omega}}_{c}$ is the cyclotron frequency and ${\ensuremath{\omega}}_{0}$ is the LO-phonon frequency). Existing results are rederived and generalized.