Inducing topological order in a honeycomb lattice

TL;DR

This paper proposes a method to induce topological insulator phases in a honeycomb lattice by coupling it to a metallic environment, using long-range interactions controlled by the metal's Fermi wave vector, with potential realization in cold-atom systems.

Contribution

It introduces a novel approach to generate topological order in honeycomb lattices via metallic environment-induced interactions without spin-orbit coupling.

Findings

Fermi wave vector kF controls the phase of the honeycomb lattice.

Tuning parameters can realize topological insulator and quantum Hall states.

Parameter estimates suggest feasibility in cold-atom experiments.

Abstract

We explore the possibility of inducing a topological insulator phase in a honeycomb lattice lacking spin-orbit interaction using a metallic (or Fermi gas) environment. The lattice and the metallic environment interact through a density-density interaction without particle tunneling, and integrating out the metallic environment produces a honeycomb sheet with in-plane oscillating long-ranged interactions. We find the ground state of the interacting system in a variational mean-field method and show that the Fermi wave vector, kF, of the metal determines which phase occurs in the honeycomb lattice sheet. This is analogous to the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism in which the metal's kF determines the interaction profile as a function of the distance. Tuning kF and the interaction strength may lead to a variety of ordered phases, including a topological insulator and anomalous quantum-hall states with complex next-nearest-neighbor hopping, as in the Haldane and the Kane-Mele model. We estimate the required range of parameters needed for the topological state and find that the Fermi vector of the metallic gate should be of the order of 3Pi/8a (with a being the graphene lattice constant). The net coupling between the layers, which includes screening in the metal, should be of the order of the honeycomb lattice bandwidth. This configuration should be most easily realized in a cold-atoms setting with two interacting Fermionic species.