SciPost Physics

SciPost Phys. 7, 048 (2019) · published 10 October 2019

• doi: 10.21468/SciPostPhys.7.4.048
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Abstract

We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation -- technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer graphene as well as many generalizations and extensions of it. The derivation is carried out entirely in real space.

• Samajdar et al., Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene
  Phys. Rev. B 102, 064501 (2020) [Crossref]
• Luo et al., Magic continuum in a twisted bilayer square lattice with staggered flux
  Phys. Rev. B 104, 035136 (2021) [Crossref]
• Ying et al., Current switching of valley polarization in twisted bilayer graphene
  Phys. Rev. B 103, 115436 (2021) [Crossref]
• Vogl et al., Effective Floquet Hamiltonians for periodically driven twisted bilayer graphene
  Phys. Rev. B 101, 235411 (2020) [Crossref]
• Zhu et al., Magnon bands in twisted bilayer honeycomb quantum magnets*
  Chinese Phys. B 30, 077505 (2021) [Crossref]
• Mannaï et al., Twistronics versus straintronics in twisted bilayers of graphene and transition metal dichalcogenides
  Phys. Rev. B 103, L201112 (2021) [Crossref]
• Zeng et al., Formation of topological domain walls and quantum transport properties of zero-line modes in commensurate bilayer graphene systems
  Front. Phys. 17, 63503 (2022) [Crossref]
• Hejazi et al., Noncollinear phases in moiré magnets
  Proc. Natl. Acad. Sci. U.S.A. 117, 10721 (2020) [Crossref]
• Parhizkar et al., Strained bilayer graphene, emergent energy scales, and moiré gravity
  Phys. Rev. Research 4, L022027 (2022) [Crossref]
• Slagle et al., Charge transfer excitations, pair density waves, and superconductivity in moiré materials
  Phys. Rev. B 102, 235423 (2020) [Crossref]
• Carr et al., Duality between atomic configurations and Bloch states in twistronic materials
  Phys. Rev. Research 2, 033162 (2020) [Crossref]
• Vafek et al., Continuum effective Hamiltonian for graphene bilayers for an arbitrary smooth lattice deformation from microscopic theories
  Phys. Rev. B 107, 075123 (2023) [Crossref]
• Kumar et al., Fractal non-Fermi liquids from moiré Hofstadter phonons
  Phys. Rev. B 102, 235120 (2020) [Crossref]
• Aggarwal et al., A primer on twistronics: a massless Dirac fermion’s journey to moiré patterns and flat bands in twisted bilayer graphene
  J. Phys.: Condens. Matter 35, 143001 (2023) [Crossref]
• Rodriguez-Vega et al., Floquet engineering of twisted double bilayer graphene
  Phys. Rev. Research 2, 033494 (2020) [Crossref]
• Wagner et al., Landau levels in curved space realized in strained graphene
  SciPost Phys. Core 5, 029 (2022) [Crossref]
• Ma et al., Effective curved space-time geometric theory of generic-twist-angle graphene with application to a rotating bilayer configuration
  Phys. Rev. B 105, 245102 (2022) [Crossref]
• Eugenio et al., Twisted-bilayer FeSe and the Fe-based superlattices
  SciPost Phys. 15, 081 (2023) [Crossref]
• Roberts et al., Analog gravity and continuum effective theory of the graphene tight-binding lattice model
  Phys. Rev. B 109, 045425 (2024) [Crossref]
• Kang et al., Cascades between Light and Heavy Fermions in the Normal State of Magic-Angle Twisted Bilayer Graphene
  Phys. Rev. Lett. 127, 266402 (2021) [Crossref]
• Chaudhary et al., Twisted bilayers of thin film magnetic topological insulators
  Phys. Rev. Research 4, 043034 (2022) [Crossref]
• Jankowski et al., Polarization textures in crystal supercells with topological bands
  Phys. Rev. B 110, 085429 (2024) [Crossref]
• Bennett et al., Theory of polarization textures in crystal supercells
  Phys. Rev. Research 5, 033216 (2023) [Crossref]
• Becker et al., Spectral characterization of magic angles in twisted bilayer graphene
  Phys. Rev. B 103, 165113 (2021) [Crossref]
• Vafek et al., Renormalization Group Study of Hidden Symmetry in Twisted Bilayer Graphene with Coulomb Interactions
  Phys. Rev. Lett. 125, 257602 (2020) [Crossref]
• Kong et al., Modeling of Electronic Dynamics in Twisted Bilayer Graphene
  SIAM J. Appl. Math. 84, 1011 (2024) [Crossref]
• Guerci et al., Nature of even and odd magic angles in helical twisted trilayer graphene
  Phys. Rev. B 109, 205411 (2024) [Crossref]
• Walet et al., Flat bands, strains, and charge distribution in twisted bilayer h−BN
  Phys. Rev. B 103, 125427 (2021) [Crossref]
• Guerci et al., Designer meron lattice on the surface of a topological insulator
  Phys. Rev. B 106, 245417 (2022) [Crossref]
• Halbertal et al., Multilayered Atomic Relaxation in van der Waals Heterostructures
  Phys. Rev. X 13, 011026 (2023) [Crossref]
• Benschop et al., Measuring local moiré lattice heterogeneity of twisted bilayer graphene
  Phys. Rev. Research 3, 013153 (2021) [Crossref]
• Rademaker et al., Topological flat bands and correlated states in twisted monolayer-bilayer graphene
  Phys. Rev. Research 2, 033150 (2020) [Crossref]
• Rodriguez-Vega et al., Low-frequency and Moiré–Floquet engineering: A review
  Annals of Physics 435, 168434 168434 (2021) [Crossref]
• Parhizkar et al., Generic topological criterion for flat bands in two dimensions
  Phys. Rev. B 110, L121111 (2024) [Crossref]
• Kolář et al., Anderson’s Theorem for Correlated Insulating States in Twisted Bilayer Graphene
  Phys. Rev. Lett. 130, 076204 (2023) [Crossref]
• Putzer et al., Band theory for heterostructures with interface superlattices
  Phys. Rev. B 110, 125143 (2024) [Crossref]
• Koshino et al., Effective continuum model for relaxed twisted bilayer graphene and moiré electron-phonon interaction
  Phys. Rev. B 101, 195425 (2020) [Crossref]
• Kang et al., Pseudomagnetic fields, particle-hole asymmetry, and microscopic effective continuum Hamiltonians of twisted bilayer graphene
  Phys. Rev. B 107, 075408 (2023) [Crossref]
• Brillaux et al., Analytical renormalization group approach to competing orders at charge neutrality in twisted bilayer graphene
  Phys. Rev. Research 4, 033168 (2022) [Crossref]