Addition spectra of arrays of interacting quantum dots: Dependence on array geometry and magnetic field

We use the extended Hubbard model to calculate the addition spectra of line ar chains and ring-shaped arrays of three, four, and five quantum dots. We fmd that for linear arrays, the addition spectra obtained with the pure Hub bard model and the pure charging model show no qualitative differences. For rings of quantum dots, however, the Hubbard model always produces doubly d egenerate states that are absent in the charging model. We attribute the do uble degeneracy to the presence of a periodic boundary condition. The degen eracies are lifted by a perpendicular magnetic field (B) over right arrow. As (B) over right arrow varies, the spectra are periodic with a period of o ne magnetic Aux quantum phi(0) = h/e and symmetric about one-half magnetic Bur quantum enclosed by the ring of quantum dots. [S0163-12529(98)03344-X].