Inducing topological order in a honeycomb lattice

Understand

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.