ADDITION SPECTRUM, PERSISTENT CURRENT, AND SPIN POLARIZATION IN COUPLED QUANTUM-DOT ARRAYS - COHERENCE, CORRELATION, AND DISORDER

The ground-state persistent current and electron addition spectrum in two-dimensional quantum dot arrays and one-dimensional quantum dot rin gs, pierced by an external magnetic flux, are investigated using the e xtended Hubbard model. The collective multidot problem is shown to map exactly into the strong-field noninteracting finite-size Hofstadter b utterfly problem at the spin polarization transition. The finite-size Hofstadter problem is discussed, and an analytical solution for Limiti ng values of dux is obtained. In weak fields we predict interesting fl ux periodic oscillations in the spin component along the quantization axis with a periodicity given by vh/e (v less than or equal to 1). The sensitivity of the calculated persistent current to interaction and d isorder is shown to reflect the intricacies of various Mott-Hubbard qu antum phase transitions in two-dimensional systems: the persistent cur rent is suppressed in the antiferromagnetic Mott-insulating phase gove rned by intradot Coulomb interactions; the persistent current is maxim ized at the spin density wave-charge density wave transition driven by the nearest-neighbor interdot interaction; the Mott-insulating phase persistent current is enhanced by the long-range interdot interactions to its noninteracting value; the strong suppression of the noninterac ting current in the presence of random disorder is seen only at large disorder strengths; at half-filling even a relatively weak intradot Co ulomb interaction enhances the disordered noninteracting system persis tent current; in general, the suppression of the persistent current by disorder is less significant in the presence of the long-range interd ot Coulomb interaction.