Stabilization of Topological Insulator Emerging from Electron Correlations on Honeycomb Lattice and Its Possible Relevance in Twisted Bilayer Graphene

Abstract

Realization and design of topological insulators emerging from electron correlations, called topological Mott insulators (TMIs), is pursued by using mean-field approximations as well as multi-variable variational Monte Carlo (MVMC) methods for Dirac electrons on honeycomb lattices. The topological insulator phases predicted in the previous studies by the mean-field approximation for an extended Hubbard model on the honeycomb lattice turn out to disappear, when we consider the possibility of a long-period charge-density-wave (CDW) order taking over the TMI phase. Nevertheless, we further show that the TMI phase is still stabilized when we are able to tune the Fermi velocity of the Dirac point of the electron band. Beyond the limitation of the mean-field calculation, we apply the newly developed MVMC to make accurate predictions after including the many-body and quantum fluctuations. By taking the extrapolation to the thermodynamic and weak external field limit, we present realistic criteria for the emergence of the topological insulator caused by the electron correlations. By suppressing the Fermi velocity to a tenth of that of the original honeycomb lattice, the topological insulator emerges in an extended region as a spontaneous symmetry breaking surviving competitions with other orders. We discuss experimental ways to realize it in a bilayer graphenesystem.

9 pages, 7 figures

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• Emergent lattices with geometrical frustration in doped extended Hubbard models
• Novel criticality of Dirac fermions in the presence of emergent gauge fields
• Novel criticality of Dirac fermions from lattice symmetry breaking
• Chiral topological phases in optical lattices without synthetic fields
• Hidden Charge Order of Interacting Dirac Fermions on the Honeycomb Lattice
• Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction
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