Topological Insulators and Mott Physics from the Hubbard Interaction

TL;DR

This paper explores the interplay of topology and strong interactions in the Hubbard model on a honeycomb lattice, revealing persistent topological phases, a Mott transition, and potential fractionalized topological insulators.

Contribution

It combines multiple theoretical techniques to analyze topological insulators under strong interactions, identifying new phases and transitions.

Findings

Topological phase persists under strong interactions.

Mott transition localizes charge but preserves spin structure.

Potential for fractionalized topological insulator with gapless edge spinons.

Abstract

We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions. Applying a combination of Hartree-Fock theory, slave-rotor techniques, and topological arguments, we show that the topological band insulating phase persists up to quite strong interactions. Then we apply the slave-rotor mean-field theory and find a Mott transition at which the charge degrees of freedom become localized on the lattice sites. The spin degrees of freedom, however, are still described by the original Kane-Mele band structure. Gauge field effects in this region play an important role. When the honeycomb layer is isolated then the spin sector becomes already unstable toward an easy plane Neel order. In contrast, if the honeycomb lattice is surrounded by extra "screening" layers with gapless spinons, then the system will support a fractionalized topological insulator phase with gapless spinons at the edges. For large interactions, we derive an effective spin Hamiltonian.