TSTG II: Projected Hartree-Fock Study of Twisted Symmetric Trilayer Graphene

Fang Xie; Nicolas Regnault; Dumitru Călugăru; B. Andrei Bernevig; Biao Lian

doi:10.1103/PhysRevB.104.115167

paper

TSTG II: Projected Hartree-Fock Study of Twisted Symmetric Trilayer Graphene

arXiv:2106.14905 · doi:10.1103/PhysRevB.104.115167

Abstract

The Hamiltonian of the magic-angle twisted symmetric trilayer graphene (TSTG) can be decomposed into a TBG-like flat band Hamiltonian and a high-velocity Dirac fermion Hamiltonian. We use Hartree-Fock mean field approach to study the projected Coulomb interacting Hamiltonian of TSTG developed in Călugăru et al. [Phys. Rev. B 103, 195411 (2021)] at integer fillings $ν = - 3, - 2, - 1$ and $0$ measured from charge neutrality. We study the phase diagram with $w_{0} / w_{1}$ , the ratio of $AA$ and $A B$ interlayer hoppings, and the displacement field, which introduces an interlayer potential $U$ and hybridizes the TBG-like bands with the Dirac bands. At small $U$ , we find the ground states at all fillings $ν$ are in the same phases as the tensor products of a Dirac semimetal with the filling $ν$ TBG insulator ground states, which are spin-valley polarized at $ν = - 3$ , and fully (partially) intervalley coherent at $ν = - 2, 0$ ( $ν = - 1$ ) in the flat bands. An exception is $ν = - 3$ with $w_{0} / w_{1} ≳ 0.7$ , which possibly become a metal with competing orders at small $U$ due to charge transfers between the Dirac and flat bands. At strong $U$ where the bandwidths exceed interactions, all the fillings $ν$ enter a metal phase with small or zero valley polarization and intervalley coherence. Lastly, at intermediate $U$ , semimetal or insulator phases with zero intervalley coherence may arise for $ν = - 2, - 1, 0$ . Our results provide a simple picture for the electron interactions in TSTG systems, and reveal the connection between the TSTG and TBG ground states.

31 pages, 27 figures

TSTG II: Projected Hartree-Fock Study of Twisted Symmetric Trilayer Graphene

Abstract

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