Faithful tight-binding models and fragile topology of magic-angle bilayer graphene

Po, Hoi Chun; Zou, Liujun; Senthil, T.; Vishwanath, Ashvin

doi:10.1103/physrevb.99.195455

Faithful tight-binding models and fragile topology of magic-angle bilayer graphene

Journal Article · Wed May 29 00:00:00 EDT 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.99.195455· OSTI ID:1611147

Po, Hoi Chun ^[1]; Zou, Liujun ^[2]; Senthil, T. ^[3]; Vishwanath, Ashvin ^[4]

Harvard Univ., Cambridge, MA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); DOE/OSTI
Harvard Univ., Cambridge, MA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Harvard Univ., Cambridge, MA (United States)

Correlated insulators and superconductivity have been observed in “magic-angle” twisted bilayer graphene, when the nearly flat bands close to neutrality are partially filled. Here, while a momentum-space continuum model accurately describes these flat bands, interaction effects are more conveniently incorporated in tight-binding models. We have previously shown that no fully symmetric tight-binding model can be minimal, in the sense of capturing just the flat bands, so extended models are unavoidable. Here, we introduce a family of tight-binding models that capture the flat bands while simultaneously retaining all symmetries. In particular, we construct three concrete models with five, six, or ten bands per valley and per spin. These models are also faithful, in that the additional degrees of freedom represent energy bands further away from neutrality, and they serve as optimal starting points for a controlled study of interaction effects. Furthermore, our construction demonstrates the “fragile topology” of the nearly flat bands; i.e., the obstruction to constructing exponentially localized Wannier functions can be resolved when a particular set of trivial bands is added to the model.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0008739

OSTI ID:: 1611147

Alternate ID(s):: OSTI ID: 1523316

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 19 Vol. 99; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Journal Article · Wed Sep 10 00:00:00 EDT 2025 · Physical Review Research · OSTI ID:2588888

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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Band structure methods
Bilayer films
Electronic structure
Graphene
Materials science
Physics
Symmetry protected topological states
Tight-binding model
Topological materials
Wannier function methods

Faithful tight-binding models and fragile topology of magic-angle bilayer graphene

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