TY - JOUR

T1 - Magic-angle twisted symmetric trilayer graphene as a topological heavy-fermion problem

AU - Yu, Jiabin

AU - Xie, Ming

AU - Bernevig, B. Andrei

AU - Das Sarma, Sankar

N1 - Funding Information:
J.Y. thanks Yang-Zhi Chou, Seth Davis, Biao Lian, Jay D. Sau, Zhi-Da Song, and Fang Xie for helpful discussions. This work is supported by the Laboratory of Physical Sciences at the University of Maryland. J.Y. and B.A.B. were supported by DOE Grant No. DE-SC0016239. Additional support was provided by Gordon and Betty Moore Foundation through the EPiQS Initiative, Grant No. GBMF11070 and Grant No. GBMF8685 towards the Princeton theory program.
Publisher Copyright:
© 2023 American Physical Society

PY - 2023/7/15

Y1 - 2023/7/15

N2 - Recently, Song and Bernevig [ Phys. Rev. Lett. 129, 047601 (2022)0031-9007 10.1103/PhysRevLett.129.047601 ] reformulated magic-angle twisted bilayer graphene 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, and propose a low-energy Formula Presented model that reformulates magic-angle twisted symmetric trilayer graphene as heavy localized Formula Presented modes coupled to itinerant topological semimetalic Formula Presented modes and itinerant Dirac Formula Presented modes. Our Formula Presented model well reproduces the single-particle band structure of magic-angle twisted symmetric trilayer graphene at low energies for displacement field Formula Presented. By performing Hartree-Fock calculations with the Formula Presented model for Formula Presented electrons per Moiré unit cell, we reproduce all the correlated ground states obtained from the previous numerical Hartree-Fock calculations with the Bistritzer-MacDonald-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 Formula Presented 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-Formula Presented ground states at all the integer fillings of interest, and make experimental predictions of which charge-neutral states are stabilized in magnetic fields. Our Formula Presented model provides a new perspective for understanding the correlated phenomena in magic-angle twisted symmetric trilayer graphene, suggesting that the heavy fermion paradigm of Song and Bernevig [ Phys. Rev. Lett. 129, 047601 (2022)0031-9007 10.1103/PhysRevLett.129.047601 ] should be the generic underpinning of correlated physics in multilayer moire graphene structures.

AB - Recently, Song and Bernevig [ Phys. Rev. Lett. 129, 047601 (2022)0031-9007 10.1103/PhysRevLett.129.047601 ] reformulated magic-angle twisted bilayer graphene 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, and propose a low-energy Formula Presented model that reformulates magic-angle twisted symmetric trilayer graphene as heavy localized Formula Presented modes coupled to itinerant topological semimetalic Formula Presented modes and itinerant Dirac Formula Presented modes. Our Formula Presented model well reproduces the single-particle band structure of magic-angle twisted symmetric trilayer graphene at low energies for displacement field Formula Presented. By performing Hartree-Fock calculations with the Formula Presented model for Formula Presented electrons per Moiré unit cell, we reproduce all the correlated ground states obtained from the previous numerical Hartree-Fock calculations with the Bistritzer-MacDonald-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 Formula Presented 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-Formula Presented ground states at all the integer fillings of interest, and make experimental predictions of which charge-neutral states are stabilized in magnetic fields. Our Formula Presented model provides a new perspective for understanding the correlated phenomena in magic-angle twisted symmetric trilayer graphene, suggesting that the heavy fermion paradigm of Song and Bernevig [ Phys. Rev. Lett. 129, 047601 (2022)0031-9007 10.1103/PhysRevLett.129.047601 ] should be the generic underpinning of correlated physics in multilayer moire graphene structures.

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U2 - 10.1103/PhysRevB.108.035129

DO - 10.1103/PhysRevB.108.035129

M3 - Article

AN - SCOPUS:85165627426

SN - 2469-9950

VL - 108

JO - Physical Review B

JF - Physical Review B

IS - 3

M1 - 035129

ER -