Realizing Topological Mott Insulators from the RKKY Interaction

TL;DR

This paper proposes a method to realize topological Mott insulators in fermion mixtures on a honeycomb lattice by inducing effective interactions that lead to quantum anomalous Hall or spin Hall phases without external gauge fields.

Contribution

It introduces a novel approach to engineer topological phases via RKKY interactions in fermion mixtures, avoiding artificial gauge fields or spin-orbit coupling.

Findings

Effective Haldane mass induces quantum anomalous Hall effect.

Competition between Semenoff and Haldane masses analyzed.

Potential realization in optical lattices or graphene heterostructures.

Abstract

We engineer topological insulating phases in a fermion-fermion mixture on the honeycomb lattice, without resorting to artificial gauge fields or spin-orbit couplings and considering only local interactions. Essentially, upon integrating out the fast component (characterized by a larger hopping amplitude) in a finite region of dopings, we obtain an effective interaction between the slow fermions at half-filling, which acquires a Haldane mass with opposite parity in the two valleys of the Dirac cones, thus triggering a quantum anomalous Hall effect. We carefully analyze the competition between the induced Semenoff-type mass (producing charge density wave orders in real space) versus the Haldane mass (quantum anomalous Hall phase), as a function of the chemical potential of the fast fermions. If the second species involves spin-1/2 particles, this interaction may induce a quantum spin Hall phase. Such fermion-fermion mixtures can be realized in optical lattices or in graphene heterostructures.