Broken Generalized Kohn Theorem in Harmonic Dot Lattices due to Coulomb Interaction between the Dots: Exact solution of the Schrödinger equation in the dipole approximation

Abstract

The Generalized Kohn Theorem in arrays of parabolic quantum dots with Coulomb interaction between the dots is violated, if there are different dot species involved. We solve the Schrödinger equation for cubic lattices with two different dots per unit cell: i) two different circular dots and ii) two elliptical dots, which are rotated by $90^o$ relative to each other. The interaction between the dots is considered in dipole approximation and long-- wavelength excitation spectra including FIR intensities are calculated. The energy spectrum of the first case can be expressed as a superposition of two noninteracting dots with an effective confinement frequency, which includes the effect of dot interaction. Only in the second case a splitting of degenerate absorption lines (versus magnetic field) occurs, which is a qualitative indication for interdot interaction. If the interaction becomes very strong and if all lattice sites (not necessarily confinement potentials) are equivalent, then the contribution of the dot interaction over-plays possible differences in the confinement potentials and the Kohn Theorem gradually re-entries, in the sense that one pair of excitation modes (pseudo Kohn modes) becomes independent of the interaction strength.