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Inducing topological order in a honeycomb lattice

Pereg-Barnea, T. and Refael, G. (2012) Inducing topological order in a honeycomb lattice. Physical Review B, 85 (7). Art. No. 075127 . ISSN 1098-0121. doi:10.1103/PhysRevB.85.075127.

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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 k_F 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 k_F determines the interaction profile as a function of the distance. Tuning k_F 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 3π/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.

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Additional Information:© 2012 American Physical Society. Received 23 November 2010; revised manuscript received 7 February 2012; published 22 February 2012. The authors would like to acknowledge useful discussions with J. Alicea, M. Franz, J. Lau, N. H. Lindner, and J. Simon. G.R. is grateful for the generous support of the Packard Foundation and the FENA Focus Center, one of six research centers funded under the Focus Center Research Program (FCRP), a Semiconductor Research Corporation entity. T.P.B. and G.R are supported by the Research Corporation Cottrell Scholars Award, and DARPA. T.P.B. was also supported by the National Science and Engineering Council of Canada.
Funding AgencyGrant Number
Packard FoundationUNSPECIFIED
Focus Center Research Program (FCRP) FENA Focus CenterUNSPECIFIED
Research Corporation Cottrell Scholars AwardUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
National Science and Engineering Council of Canada (NSERC)UNSPECIFIED
Issue or Number:7
Classification Code:PACS: 71.10.Fd, 71.10.Hf, 71.10.Pm
Record Number:CaltechAUTHORS:20120321-105734817
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29799
Deposited By: Tony Diaz
Deposited On:21 Mar 2012 20:18
Last Modified:09 Nov 2021 19:30

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