Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions
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PhysRevB.98.085435.pdf
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Author(s)
Zou, Liujun
Po, Hoi Chun
Vishwanath, Ashvin
Senthil, T.
Date Issued
August 2018
Journal
Physical Review B
Publisher
American Physical Society
Citation
Zou, Liujun et al. "Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions." Physical Review B 98, 8 (August 2018): 085435 © 2018 American Physical Society
Version
Final published version
Abstract
A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (e.g. θ∼1.05[superscript ∘]). In this regime, correlated insulating states and superconductivity have been experimentally observed. A microscopic description of these phenomena requires an understanding of universal aspects of the band structure, which we discuss here. First, we point out the importance of emergent symmetries, such as valley conservation, which are excellent symmetries in the limit of small twist angles and dictate qualitative features of the band structure. These have sometimes been overlooked when discussing commensurate approximants to the band structure, which we also review here, and solidify their connection with the continuum theory which incorporates all emergent symmetries. Finally, we discuss obstructions to writing tight-binding models of just the isolated bands, and in particular a symmetry-based diagnostic of these obstructions, as well as relations to band topology and strategies for resolving the obstruction. Especially, we construct a four-band model where the two lower isolated bands realize all identified Wannier obstructions of the single-valley nearly flat bands of twisted bilayer graphene.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.98.085435
