TY - JOUR

T1 - Twisted bilayer graphene as topological heavy fermion

T2 - II. Analytical approximations of the model parameters

AU - Călugăru, Dumitru

AU - Borovkov, Maksim

AU - Lau, Liam L.H.

AU - Coleman, Piers

AU - Song, Zhi Da

AU - Bernevig, B. Andrei

N1 - Funding Information:
The simulations presented in this work were performed using the Princeton Research Computing resources at Princeton University, which is a consortium of groups led by the Princeton Institute for Computational Science and Engineering (PICSciE) and Office of Information Technology’s Research Computing. D.C. and B.A.B. were primarily supported by the DOE Grant No. DE-SC0016239, the Simons Investigator Grant No. 404513, the Gordon and Betty Moore Foundation through Grant No. GBMF8685 towards the Princeton theory program, and the Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant No. GBMF11270). D.C. acknowledges the hospitality of the Donostia International Physics Center, at which part of this work was carried out. L.L.H.L. and P.C. are supported by the Office of Basic Energy Sciences, Material Sciences and Engineering Division, U.S. Department of Energy (DOE) under Contract DE-FG02-101ER45792. Z.-D. S. was supported by National Natural Science Foundation of China (General Program No. 12474005), National Key Research and Development Program of China (No. 2021YFA1401920).
Funding Information:
The simulations presented in this work were performed using the Princeton Research Computing resources at Princeton University, which is a consortium of groups led by the Princeton Institute for Computational Science and Engineering (PICSciE) and Office of Information Technology’s Research Computing. D.C. and B.A.B. were primarily supported by the DOE Grant No. DE-SC0016239, the Simons Investigator Grant No. 404513, the Gordon and Betty Moore Foundation through Grant No. GBMF8685 towards the Princeton theory program, and the Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant No. GBMF11270). D.C. acknowledges the hospitality of the Donostia International Physics Center, at which part of this work was carried out. L.L.H.L. and P.C. are supported by the Office of Basic Energy Sciences, Material Sciences and Engineering Division, U.S. Department of Energy (DOE) under Contract DE-FG02-101ER45792. Z.-D. S. was supported by National Natural Science Foundation of China (General Program No. 12474005), National Key Research and Development Program of China (No. 2021YFA1401920).
Publisher Copyright:
© 2023 Author(s).

PY - 2023/6/1

Y1 - 2023/6/1

N2 - The recently-introduced topological heavy fermion (THF) model [1] of twisted bilayer graphene (TBG) aims to reconcile the quantum-dot-like electronic structure of the latter observed by scanning tunneling microscopy, with its electron delocalization seen in transport measurements. The THF model achieves this by coupling localized (heavy) fermions with anomalous conduction electrons. Originally, the parameters of the THF model were obtained numerically from the Bistritzer-Macdonald (BM) model of TBG [1]. In this work, we derive analytical expressions for the THF model parameters as a function of the twist angle, the ratio between the tunneling amplitudes at the AA and AB regions (w0/w1), and the screening length of the interaction potential. By numerically computing the THF model parameters across an extensive experimentally-relevant parameter space, we show that the resulting approximations are remarkably good, i.e., within the 30% relative error for almost the entire parameter space. At the single-particle level, the THF model accurately captures the energy spectrum of the BM model over a large phase space of angles and tunneling amplitude ratios. When interactions are included, we also show that the THF description of TBG is good around the magic angle for realistic values of the tunneling amplitude ratios (0.6 ≤ w0/w1 ≤ 1.0), for which the hybridization between the localized and conduction fermions γ is smaller than the onsite repulsion of the heavy fermions U1 (i.e., |γ| < U1).

AB - The recently-introduced topological heavy fermion (THF) model [1] of twisted bilayer graphene (TBG) aims to reconcile the quantum-dot-like electronic structure of the latter observed by scanning tunneling microscopy, with its electron delocalization seen in transport measurements. The THF model achieves this by coupling localized (heavy) fermions with anomalous conduction electrons. Originally, the parameters of the THF model were obtained numerically from the Bistritzer-Macdonald (BM) model of TBG [1]. In this work, we derive analytical expressions for the THF model parameters as a function of the twist angle, the ratio between the tunneling amplitudes at the AA and AB regions (w0/w1), and the screening length of the interaction potential. By numerically computing the THF model parameters across an extensive experimentally-relevant parameter space, we show that the resulting approximations are remarkably good, i.e., within the 30% relative error for almost the entire parameter space. At the single-particle level, the THF model accurately captures the energy spectrum of the BM model over a large phase space of angles and tunneling amplitude ratios. When interactions are included, we also show that the THF description of TBG is good around the magic angle for realistic values of the tunneling amplitude ratios (0.6 ≤ w0/w1 ≤ 1.0), for which the hybridization between the localized and conduction fermions γ is smaller than the onsite repulsion of the heavy fermions U1 (i.e., |γ| < U1).

KW - Bistritzer-Macdonald model

KW - anomalous conduction electrons.

KW - localized fermions

KW - topological heavy fermion model

KW - twisted bilayer graphene

UR - http://www.scopus.com/inward/record.url?scp=85163957995&partnerID=8YFLogxK

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U2 - 10.1063/10.0019421

DO - 10.1063/10.0019421

M3 - Article

AN - SCOPUS:85163957995

SN - 1063-777X

VL - 49

SP - 640

EP - 654

JO - Low Temperature Physics

JF - Low Temperature Physics

IS - 6

ER -