Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene

Venderbos, Jörn W. F.; Fernandes, Rafael M.

doi:10.1103/physrevb.98.245103

Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene

Journal Article · Sun Dec 02 23:00:00 EST 2018 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.98.245103· OSTI ID:1611767

Venderbos, Jörn W. F. ^[1]; Fernandes, Rafael M. ^[2]

Univ. of Pennsylvania, Philadelphia, PA (United States); DOE/OSTI
Univ. of Minnesota, Minneapolis, MN (United States)

The recent observation of superconductivity in proximity to an insulating phase in twisted bilayer graphene (TBG) at small “magic” twist angles has been linked to the existence of nearly flat bands, which make TBG a fresh playground to investigate the interplay between correlations and superconductivity. The low-energy narrow bands were shown to be well described by an effective tight-binding model on the honeycomb lattice (the dual of the triangular Moiré superlattice) with a local orbital degree of freedom. In this paper, we perform a strong-coupling analysis of the proposed (p_x,p_y) two-orbital extended Hubbard model on the honeycomb lattice. By decomposing the interacting terms in the particle-particle and particle-hole channels, we classify the different possible superconducting, magnetic, and charge instabilities of the system. In the pairing case, we pay particular attention to the two-component (d–wave) pairing channels, which admit vestigial phases with nematic or chiral orders, and study their phenomenology. Furthermore, we explore the strong-coupling regime by obtaining a simplified spin-orbital exchange model which may describe a putative Mott-type insulating state at quarter-filling. Our mean-field solution reveals a rich intertwinement between ferromagnetic and antiferromagnetic orders with different types of nematic and magnetic orbital orders. Altogether, our work provides a solid framework for further investigations of the phase diagram of the two-orbital extended Hubbard model in both strong- and weak-coupling regimes.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0012336

OSTI ID:: 1611767

Alternate ID(s):: OSTI ID: 1484319

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 24 Vol. 98; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Ferromagnetic Mott state in Twisted Graphene Bilayers at the Magic Angle Seo, Kangjun; Kotov, Valeri N.; Uchoa, Bruno Physical Review Letters, Vol. 122, Issue 24 https://doi.org/10.1103/physrevlett.122.246402	journal	June 2019
Valence Bond Orders at Charge Neutrality in a Possible Two-Orbital Extended Hubbard Model for Twisted Bilayer Graphene Da Liao, Yuan; Meng, Zi Yang; Xu, Xiao Yan Physical Review Letters, Vol. 123, Issue 15 https://doi.org/10.1103/physrevlett.123.157601	journal	October 2019
Twisted bilayer graphene aligned with hexagonal boron nitride: Anomalous Hall effect and a lattice model Zhang, Ya-Hui; Mao, Dan; Senthil, T. Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/physrevresearch.1.033126	journal	November 2019
Quantum Valley Hall Effect, Orbital Magnetism, and Anomalous Hall Effect in Twisted Multilayer Graphene Systems Liu, Jianpeng; Ma, Zhen; Gao, Jinhua Physical Review X, Vol. 9, Issue 3 https://doi.org/10.1103/physrevx.9.031021	journal	August 2019
Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene Sharpe, Aaron L.; Fox, Eli J.; Barnard, Arthur W. Science, Vol. 365, Issue 6453 https://doi.org/10.1126/science.aaw3780	journal	July 2019
Ground state superconducting pair correlations in twisted bilayer graphene Zhang, Lufeng; Huang, Tongyun; Liang, Ying Modern Physics Letters B, Vol. 34, Issue 01 https://doi.org/10.1142/s0217984920500165	journal	December 2019
Charge-transfer insulation in twisted bilayer graphene Rademaker, Louk; Mellado, Paula arXiv https://doi.org/10.48550/arxiv.1805.05294	text	January 2018
Pressure-Induced Metal-Insulator Transition in Twisted Bi-layer Graphene Padhi, Bikash; Phillips, Philip arXiv https://doi.org/10.48550/arxiv.1810.00884	text	January 2018
The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase Liu, Jianpeng; Liu, Junwei; Dai, Xi arXiv https://doi.org/10.48550/arxiv.1810.03103	text	January 2018
Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene Kozii, Vladyslav; Isobe, Hiroki; Venderbos, Jörn W. F. arXiv https://doi.org/10.48550/arxiv.1810.04159	text	January 2018
Phonon-induced giant linear-in-$T$ resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity Wu, Fengcheng; Hwang, Euyheon; Sarma, Sankar Das arXiv https://doi.org/10.48550/arxiv.1811.04920	text	January 2018
Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene Wu, Fengcheng arXiv https://doi.org/10.48550/arxiv.1811.10620	text	January 2018
Ferromagnetic Mott State in Twisted Graphene Bilayers at the Magic Angle Seo, Kangjun; Kotov, Valeri N.; Uchoa, Bruno arXiv https://doi.org/10.48550/arxiv.1812.02550	text	January 2018
Magic of high order van Hove singularity Yuan, Noah F. Q.; Isobe, Hiroki; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1901.05432	text	January 2019
Designing Flat Band by Strain Bi, Zhen; Yuan, Noah F. Q.; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1902.10146	text	January 2019
Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems Liu, Jianpeng; Ma, Zhen; Gao, Jinhua arXiv https://doi.org/10.48550/arxiv.1903.10419	text	January 2019
Identification of superconducting pairing symmetry in twisted bilayer graphene using in-plane magnetic field and strain Wu, Fengcheng; Sarma, Sankar Das arXiv https://doi.org/10.48550/arxiv.1904.07875	text	January 2019

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