Correlation effect in topological insulators and multi-component systems is investigated. In topological insulators we focus on the coexistence of long-range magnetic ordering and non-trivial topology of the ground state. It is studied based on a combination between the Kane-Mele and double exchange models. Using the dynamical mean-field theory we found a half topological state, where electrons with one spin orientation occupy a nontrivial topological insulating state, while electrons with opposite orientation occupy another insulating state with trivial topology. In multi-component systems we focus on the Mott insulator transitions. The Mott transitions are classified by the change in the number of distinct kinds of doublons across the transition.

We observe a different Mott transition between partially localized states in which the particle components (flavors), which form the doublons, are swapped with each other but the number of distinct kinds of doublons is unchanged across the transition. The swap Mott transition occurs as a result of the competition between the Brinkman-Rice and the Falicov-Kimball localizations and the mass imbalance of the mobile particles.

References:

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2. Minh-Tien Tran and Thanh-Mai Thi Tran, J. Phys.: Condens. Matt. 34, 275603 (2022).
3. Duc-Anh Le at al, Phys. Rev. B 109, 115105 (2024).