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 two (or more than two) 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 the Mott-insulator-like state to a correlated semi-metallic state via charge-bond-order route. In the presence of magnetic field, td is complex due to the appearance of Peierls phase factor. 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 indicates that, while for the tunable parameter d = (2td/U0) greater than unity only the possibility of the triplet bound state formation exists, for d less than one both triplet and singlet states are possible. The bound states are formed due to tunneling and capacitive dot-bondings with coulomb interactions (U,U1) playing marginal role. The interaction U, however, is found to play, together with complex td, an important role in the evolution of the double quantum dot system from the insulator-like state to that of a correlated semi-metallic state through charge-bond-ordering route.