Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene

Xu, Xiao Yan; Law, K. T.; Lee, Patrick A.

doi:10.1103/physrevb.98.121406

Cited by 169 publications

(114 citation statements)

References 45 publications

(82 reference statements)

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“…Finally, we discuss the robustness of results that rely on a particular Wannier function to describe superconductivity [39,51,[53][54][55][56][57][58][59][60][61][62][63]. We shall argue that the electronassisted hopping model of Ref.…”

Section: Introductionmentioning

confidence: 97%

Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters

2019

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We analyze a description of twisted graphene bilayers, that incorporates the deformation of the layers using state of the art interlayer atomic potentials, and a modification of the hopping parameters between layers in the light of the classic Slonczewski-Weiss-McClure parametrisation. We obtain narrow bands in all cases, but that their nature can be rather different. We will show how to describe the results by equivalent continuum models. Even though such models can be constructed, their complexity can vary, requiring many coupling parameters to be included, and the full in-layer dispersion must be taken into account. The combination of all these effects will have a large impact on the wave functions of the flat bands, and that modifications in details of the underlying models can lead to significant changes. A robust conclusion is that the natural strength of the interlayer couplings is higher than usually assumed, leading to shifts in the definition of the magic angles. The structure at the edges of the narrow bands, at the Γ point of the Brillouin Zone is also strongly dependent on parametrization. As a result, the existence, and size, of band gaps between the flat bands and the neighboring ones are changed. Hence, the definition of Wannier functions, and descriptions based on local interactions are strongly dependent on the description of the model at the atomic scale. * Francisco. Guinea@imdea.org † Niels.Walet@manchester.ac.uk; https://www.research.manchester.ac.uk/portal/niels.walet.html AA AB FIG. 1. Examples of a graphene bilayer in (approximate) AA and AB alignment. arXiv:1903.00364v2 [cond-mat.str-el]

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Section: Introductionmentioning

confidence: 97%

Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters

2019

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“…An example of a four fermion interaction term, which is beyond the extended Hubbard model, appearing in the strong coupling Hamiltonian Eqs. (6,(9)(10)(11), is also shown schematically.…”

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confidence: 99%

Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands

2019

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We identify states favored by Coulomb interactions projected onto the Wannier basis of the four narrow bands of the "magic angle" twisted bilayer graphene. At the filling of two electrons/holes per moire unit cell, such interactions favor an insulating SU (4) ferromagnet. The kinetic terms select the ground state in which the two valleys with opposite spins are equally mixed, with vanishing magnetic moment per particle. We also find extended excited states, the gap to which decreases in magnetic field. An insulating stripe ferromagnetic phase is favored at one electron/hole per unit cell.r )c σ (r ) . (2) arXiv:1810.08642v1 [cond-mat.str-el]

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“…[1,2]. The origin of magic-angle phenomena, i.e., the emergence of superconductivity and correlated insulator, is now under intensive study [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

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confidence: 99%

Magic of high-order van Hove singularity

Yuan¹,

Isobe²,

Fu³

2019

Nat Commun

152

153

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The van Hove singularity in density of states generally exists in periodic systems due to the presence of saddle points of energy dispersion in momentum space. We introduce a new type of van Hove singularity in two dimensions, resulting from high-order saddle points and exhibiting power-law divergent density of states. We show that high-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field. Correlation effects from high-order van Hove singularity near Fermi level are also discussed.

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Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene

Cited by 169 publications

References 45 publications

Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters

Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters

Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands

Magic of high-order van Hove singularity

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