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Condensed Matter > Mesoscale and Nanoscale Physics
Title: Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem
(Submitted on 10 Jan 2023 (v1), last revised 18 Aug 2023 (this version, v2))
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 $f-c-d$ model that reformulates MATSTG as heavy localized $f$ modes coupled to itinerant topological semimetalic $c$ modes and itinerant Dirac $d$ modes. Our $f-c-d$ model well reproduces the single-particle band structure of MATSTG at low energies for displacement field $\mathcal{E}\in[0,300]$meV. By performing Hartree-Fock calculations with the $f-c-d$ model for $\nu=0,-1,-2$ electrons per Moir\'e 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 $f-c-d$ 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-$\mathcal{E}$ ground states at all the integer fillings of interest, and make experimental predictions of which charge-neutral states are stabilized in magnetic fields. Our $f-c-d$ 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.
Submission history
From: Jiabin Yu [view email][v1] Tue, 10 Jan 2023 19:00:21 GMT (882kb,D)
[v2] Fri, 18 Aug 2023 17:38:10 GMT (775kb,D)
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