Twisted symmetric trilayer graphene. II. Projected Hartree-Fock study

Journal Article · Thu Sep 30 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.104.115167· OSTI ID:1852151

Xie, Fang ^[1]; Regnault, Nicolas ^[2]; Călugăru, Dumitru ^[3]; Bernevig, B. Andrei ^[4]; Lian, Biao ^[3]

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1. Princeton Univ., NJ (United States); OSTI
2. Princeton Univ., NJ (United States); Sorbonne Univ., Paris (France)
3. Princeton Univ., NJ (United States)
4. Princeton Univ., NJ (United States); Donostia International Physics Center (DIPC), San Sebastian (Spain); Basque Foundation for Science, Bilbao (Spain)

The Hamiltonian of the magic-angle twisted symmetric trilayer graphene (TSTG) can be decomposed into a twisted-bilayer-graphene- (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 Calugaru 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 w₀/w₁, the ratio of AA and AB 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 w₀/w₁ ≳ 0.7 , which possibly becomes 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. Finally, our results provide a simple picture for the electron interactions in TSTG systems, and reveal the connection between the TSTG and TBG ground states.

• Research Organization: Princeton Univ., NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC); US Department of the Navy, Office of Naval Research (ONR); Schmidt Fund; National Science Foundation (NSF); Gordon and Betty Moore Foundation; BSF Israel US Foundation; Alfred P. Sloan Foundation
• Grant/Contract Number: SC0016239
• OSTI ID: 1852151
• Alternate ID(s): OSTI ID: 1833897
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 11 Vol. 104; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

2-dimensional systems
36 MATERIALS SCIENCE
Hartree-Fock methods
electronic structure
graphene
materials science
physics
strong interaction