Higher-order topological insulator in a modified Haldane-Hubbard model

TL;DR

This paper explores a modified Haldane-Hubbard model revealing a higher-order topological insulator with corner modes, robust to interactions, and identifies a topological Mott insulator with coexisting charge order.

Contribution

It introduces a modified model exhibiting higher-order topological phases and demonstrates the robustness of corner modes against interactions, also discovering a topological Mott insulator with symmetry-breaking.

Findings

Existence of corner modes in the non-interacting limit.

Robustness of topological states to finite interactions.

Identification of a topological Mott insulator with charge-density-wave order.

Abstract

We investigate the ground-state phase diagram of a modified spinless Haldane-Hubbard model with broken threefold rotational symmetry, employing exact diagonalization calculations. The interplay of asymmetry, interactions, and topology gives rise to a rich phase diagram. The non-interacting limit of the Hamiltonian exhibits a higher-order topological insulator characterized by the existence of corner modes, in contrast to known chiral edge metallic states of the standard Haldane model. Our investigation demonstrates that these symmetry-protected states are robust to the presence of finite interactions. Furthermore, in certain regimes of parameters, we show that a topological Mott insulator exists in this model, where a non-trivial topological bulk coexists with an interaction-driven charge-density-wave, whose emergence is characterized by a $Z_2$-symmetry breaking within the 3$d$-Ising universality class.