Inducing topological order in a honeycomb lattice

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.

7 pages; 2 figures; Version 2 - added references; added an appendix about screening

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Cited by in corpus (10)

• Giant topological insulator gap in graphene with 5d adatoms
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
• Diagnosis of interaction-driven topological phase via exact diagonalization
• Topological crystalline insulator phase in graphene multilayers
• Quantum Anomalous Hall Insulator Stabilized By Competing Interactions
• Topological Superconductivity without Proximity Effect
• Transport through quantum spin Hall insulator/metal junctions in graphene ribbons
• Realizing Topological Mott Insulators from the RKKY Interaction
• Chiral properties of topological-state loops