Nonlocal theory of collective excitations in quantum-dot arrays.

Abstract

We present a nonlocal theory of collective excitations in quantum-dot arrays. Selection rules, oscillator strengths, and Coulomb interactions inside a dot and between dots are discussed. The collective excitation energy is found to ``saturate'' for ${\mathit{n}}_{0}$ (the number of electrons per dot) greater than 3. The depolarization energy shift in a quantum-dot array is found to be predominantly due to interdot coupling. We explain qualitatively the multiple branches and anticrossings recently observed in far-infrared experiments. We predict that anticrossings can occur only if ${\mathit{n}}_{0}$>2. If ${\mathit{n}}_{0}$\ensuremath{\le}2, there should be only one branch with positive B dispersion, and one branch with negative B dispersion, where B represents a perpendicular magnetic field. Multiple branches with positive (negative) B dispersions occur for larger ${\mathit{n}}_{0}$. The use of left (right) -circularly-polarized light should result in signals predominantly from positive (negative) B dispersion branches, while signals from the opposite polarization branches should provide information on the coupling between positive and negative B dispersion branches.