paper

Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem

arXiv:2301.04171 · doi:10.1103/PhysRevB.108.035129

Abstract

Recently, Ref. [1] reformulated magic-angle twisted bilayer graphene (MATBG) as a topological heavy fermion problem, and used this reformulation to provide a deeper understanding for the correlated phases at integer fillings. In this work, we generalize this heavy-fermion paradigm to magic-angle twisted symmetric trilayer graphene (MATSTG), and propose a low-energy model that reformulates MATSTG as heavy localized modes coupled to itinerant topological semimetalic modes and itinerant Dirac modes. Our model well reproduces the single-particle band structure of MATSTG at low energies for displacement field meV. By performing Hartree-Fock calculations with the model for electrons per Moiré unit cell, we reproduce all the correlated ground states obtain from the previous numerical Hartree-Fock calculations with the Bistritzer-MacDonald-type (BM-type) model, and we find additional new correlated ground states at high displacement field. Based on the numerical results, we propose a simple rule for the ground states at high displacement fields by using the model, and provide analytical derivation for the rule at charge neutrality. We also provide analytical symmetry arguments for the (nearly-)degenerate energies of the high- ground states at all the integer fillings of interest, and make experimental predictions of which charge-neutral states are stabilized in magnetic fields. Our model provides a new perspective for understanding the correlated phenomena in MATSTG, suggesting that the heavy fermion paradigm of Ref. [1] should be the generic underpinning of correlated physics in multilayer moire graphene structures.

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