Polaronic effects in one-dimensional quantum antidot arrays

We study the effect of polaronic corrections arising from the electron-longitudinal optical phonon interaction on the energy spectrum of a two-dimensional electron system with a one-dimensional periodic antidot array geometry created by a weak electrostatic modulation potential, and subjected to a weak magnetic field modulation as well as a uniform strong perpendicular static magnetic field. To incorporate the effects of electron-phonon interactions within the framework of Frohlich polaron theory, we first apply a displaced-oscillator type unitary transformation to diagonalise the relevant Frohlich Hamiltonian, and we then determine the parameters of this transformation together with the parameter included in the electronic trial wave function . On the basis of this technique, it has been shown that the polaronic corrections have non-negligible effects on the electronic spectrum of a two-dimensional electron system with a quantum antidot array, since switching such an interaction results in shifting the degeneracy restoring points of Landau levels wherein the flatband condition is fulfilled, thus suppressing the Weiss oscillations.