Exact and perturbative insulator states and excitations in twisted bilayer graphene

ORAL

Abstract

We study the low energy states of the flat-band projected Hamiltonian of magic angle twisted bilayer graphene with Coulomb interactions. By treating the nonchiral interaction and the kinetic energy as perturbations, we analytically derive the exact or perturbative strongly interacting (Chern) insulator ground states at all integer fillings |\nu|<4. We find the ground state has Chern number mod(\nu,2), and is intervalley coherent (valley polarized) at fillings |\nu|=0,1,2 (|\nu|=3). We further show that the insulators have analytically computable charge 0, +-1,+-2 excitations. We show that the Goldstone modes of the ground states are quadratic. Furthermore, from the charge 1 and 2 excitations, we prove the absence of Cooper pairing from the Coulomb interaction in the flat band limit, which suggests other superconductivity mechanisms.

*DOE Grant No. DE-SC0016239, the Schmidt Fund No. 404513, and the Packard Foundation. NSF-EAGER No. DMR 1643312, NSF-MRSEC No. DMR-1420541 and DMR-2011750, ONR No. N00014-20-1-2303, Gordon and Betty Moore GBMF8685, BSF No. 2018226, and the Princeton Global Network Funds, No. ANR-16-CE30-0025.

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Presenters

  • Biao Lian

    • Princeton University
    • Princeton Center for Theoretical Science, Princeton University
    • Physics, Princeton University

Authors

  • Biao Lian

    • Princeton University
    • Princeton Center for Theoretical Science, Princeton University
    • Physics, Princeton University

  • Zhida Song

    • Princeton University

  • Nicolas Regnault

    • Department of Physics, Princeton University
    • Princeton University
    • Ecole Normale Superieure
    • Physics, Princeton University

  • Aditya Cowsik

    • Stanford University
    • Physics, Princeton University

  • Fang Xie

    • Princeton University
    • Physics, Princeton University

  • Dmitri K. Efetov

    • ICFO-The Institute of Photonic Sciences
    • ICFO
    • ICFO – The Institute of Photonic Sciences

  • Ali Yazdani

    • Princeton University
    • Joseph Henry Laboratories & Department of Physics, Princeton University

  • Andrei B Bernevig

    • Department of Physics, Princeton University
    • Princeton University
    • Princeto University, Princeton, USA
    • Physics, Princeton University