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Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
Abstract
For this work, we apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)], to obtain its Kondo lattice limit. In this limit localized $$\mathcal{f}$$ electrons on a triangular lattice interact with topological conduction $$\mathcal{c}$$ electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0, ±1, ±2 are controlled by the heavy $$\mathcal{f}$$ electrons, while ν=±3 is at the border of a phase transition between two $$\mathcal{f}$$-electron fillings. For ν=0, ±1, ±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the $$\mathcal{f}$$ moments in the full model and analytically prove the SU(4) Hund’s rule for the ground state which maintains that two $$\mathcal{f}$$ electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite “bond-operators” method. We then compute the excitation spectrum of the $$\mathcal{f}$$ moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the $$\mathcal{f}$$ moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.
- Authors:
-
[1];
[3]
- Donostia International Physics Center (DIPC), San Sebastian (Spain)
- Princeton Univ., NJ (United States); Donostia International Physics Center (DIPC), San Sebastian (Spain); Basque Foundation for Science, Bilbao (Spain). IKERBASQUE
- Brookhaven National Laboratory (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.
- Publication Date:
- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE); Gordon and Betty Moore Foundation; European Research Council (ERC)
- OSTI Identifier:
- 1992849
- Alternate Identifier(s):
- OSTI ID: 1985793
- Report Number(s):
- BNL-224599-2023-JAAM; BNL-224525-2023-JAAM
Journal ID: ISSN 0031-9007; TRN: US2404246
- Grant/Contract Number:
- SC0012704; SC0016239; GBMF11070
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 131; Journal Issue: 2; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; magnetism; RKKY interaction; spin fluctuations; strongly correlated systems; twisted bilayer graphene; Kondo lattice model
Citation Formats
Hu, Haoyu, Bernevig, B. Andrei, and Tsvelik, Alexei M. Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory. United States: N. p., 2023.
Web. doi:10.1103/physrevlett.131.026502.
Hu, Haoyu, Bernevig, B. Andrei, & Tsvelik, Alexei M. Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory. United States. https://doi.org/10.1103/physrevlett.131.026502
Hu, Haoyu, Bernevig, B. Andrei, and Tsvelik, Alexei M. Tue .
"Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory". United States. https://doi.org/10.1103/physrevlett.131.026502.
@article{osti_1992849,
title = {Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund’s Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory},
author = {Hu, Haoyu and Bernevig, B. Andrei and Tsvelik, Alexei M.},
abstractNote = {For this work, we apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)], to obtain its Kondo lattice limit. In this limit localized $\mathcal{f}$ electrons on a triangular lattice interact with topological conduction $\mathcal{c}$ electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0, ±1, ±2 are controlled by the heavy $\mathcal{f}$ electrons, while ν=±3 is at the border of a phase transition between two $\mathcal{f}$-electron fillings. For ν=0, ±1, ±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the $\mathcal{f}$ moments in the full model and analytically prove the SU(4) Hund’s rule for the ground state which maintains that two $\mathcal{f}$ electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite “bond-operators” method. We then compute the excitation spectrum of the $\mathcal{f}$ moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the $\mathcal{f}$ moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.},
doi = {10.1103/physrevlett.131.026502},
journal = {Physical Review Letters},
number = 2,
volume = 131,
place = {United States},
year = {Tue Jul 11 00:00:00 EDT 2023},
month = {Tue Jul 11 00:00:00 EDT 2023}
}
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