Inducement of spin-pairing and correlated semi-metallic state in Mott–Hubbard quantum dot array

We model a quantum dot-array (with one electron per dot) comprising of N⩾2 coupled dots by an extended Hubbard Hamiltonian to investigate the role played by the inter-dot tunneling amplitude td, together with intra-dot (U) and inter-dot (U1) coulomb repulsions, in the singlet/triplet bound state formation and evolution of the system from an insulator-like state to a correlated semi-metallic state in the presence of magnetic field. We introduce a short-ranged inter-dot capacitive coupling U0, assumed to be non-zero for nearest-neighbor dots only, for the bound state analysis. The study shows that for the tunable parameter δ=(2td/U0)<1 the possibility of singlet state formation exists. As regards triplet state formation, even an infinitely small value of U0 is sufficient; the coulomb interactions (U, U1) play marginal role. The interaction U, however, is found to be important in magnetic field-induced evolution of the double quantum dot system to a correlated semi-metallic state.