Magic numbers and optical-absorption spectrum in vertically coupled quantum dots in the fractional quantum Hall regime.

Abstract

Exact diagonalization is used to study the quantum states of vertically coupled quantum dots in strong magnetic fields. We find that electron correlation in the double dot leads to angular momentum magic numbers that are distinct from those of a single dot. The double dot magic numbers occur at low angular momentum and the single dot magic numbers reappear at a critical angular momentum determined by the strength of the interdot electron tunneling. We also propose that the magic numbers can be investigated experimentally in vertically coupled dots. Because of the generalized Kohn theorem, the far-infrared optical absorption spectrum of a single dot is unaffected by correlation, but the theorem does not hold for two vertically coupled dots that have different confining potentials. We show that the absorption energy of the double dot should exhibit discontinuities at the magnetic fields where the total angular momentum changes from one magic number to another. \textcopyright{} 1996 The American Physical Society.