Inducement of Spin-pairing and Correlated Semi-metallic State in Mott-Hubbard Quantum Dot Array

TL;DR

This paper models a quantum dot array using an extended Hubbard Hamiltonian to explore how inter-dot tunneling, Coulomb interactions, and magnetic fields induce spin pairing and transition from Mott-insulator to semi-metallic states.

Contribution

It introduces a comprehensive model analyzing the interplay of tunneling, Coulomb interactions, and magnetic effects in quantum dot arrays, revealing mechanisms for spin pairing and phase transitions.

Findings

Triplet bound states form when 2td/U0 > 1.

Both singlet and triplet states are possible when 2td/U0 < 1.

Coulomb interactions U and U1 have marginal effects on bound state formation.

Abstract

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.