Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime

Scheer, Michael G.; Gu, Kaiyuan; Lian, Biao

doi:10.1103/physrevb.106.115418

Cited by 14 publications

(6 citation statements)

References 95 publications

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“…The arguments given in this section are a simple generalization of those in Ref. [1] which considered the case of TBG twisted near an arbitrary commensurate angle. See also Apps.…”

Section: Appendix C: Moiré Models For Each Type Of Commensurate Confi...mentioning

confidence: 96%

“…We can write the primitive vectors for P c corresponding to au 1 + and au 2 + in the form bu 1 c,+ and bu 2 c,+ . Similarly, we can write the primitive vectors for P c corresponding to e R θ au 1 − and e R θ au 2 − in the form e − R θ bu 1 c,− and e − R θ bu 2 c,− . A simple calculation shows…”

Section: Commensuration Reciprocal Latticementioning

confidence: 99%

“…( 9) in Ref. [1]. We assume that tl ,α ,l,α (Q) depends only on |Q| and decreases rapidly as |Q| grows.…”

Section: Appendix C: Moiré Models For Each Type Of Commensurate Confi...mentioning

confidence: 99%

“…where 0 and θ 0 describe some commensurate configuration 1 . For the coupled-valley graphene model, we take…”

mentioning

confidence: 99%

“…( 71), (74), and (75) of Ref. [1] with |φ 0 | = π/2, and the T qj , S l 0 matrices have the same form as the T s,qj , S η s,0 matrices in Tab. I(a) with wm,µ = 0.…”

mentioning

confidence: 99%

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Kagome and honeycomb flat bands in moiré graphene

Scheer¹,

Lian²

2023

Preprint

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We propose a class of graphene-based moiré systems hosting flat bands on kagome and honeycomb moiré superlattices. These systems are formed by stacking a graphene layer on a 2D substrate with lattice constant approximately √ 3 times that of graphene. When the moiré potentials are induced by a 2D irreducible corepresentation in the substrate, the model shows a rich phase diagram of low energy bands including eigenvalue fragile phases as well as kagome and honeycomb flat bands. Spin-orbit coupling in the substrate can lift symmetry protected degeneracies and create spin Chern bands, and we observe spin Chern numbers up to 3. We additionally propose a moiré system formed by stacking two graphene-like layers with similar lattice constants but opposite signs of the Dirac Fermi velocity. This system exhibits multiple kagome and honeycomb flat bands simultaneously. Both models we propose resemble the hypermagic model of Ref.[1] and may provide ideal platforms for the realization of strongly correlated topological phases.

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“…The arguments given in this section are a simple generalization of those in Ref. [1] which considered the case of TBG twisted near an arbitrary commensurate angle. See also Apps.…”

Section: Appendix C: Moiré Models For Each Type Of Commensurate Confi...mentioning

confidence: 96%

Section: Commensuration Reciprocal Latticementioning

confidence: 99%

“…( 9) in Ref. [1]. We assume that tl ,α ,l,α (Q) depends only on |Q| and decreases rapidly as |Q| grows.…”

Section: Appendix C: Moiré Models For Each Type Of Commensurate Confi...mentioning

confidence: 99%

“…where 0 and θ 0 describe some commensurate configuration 1 . For the coupled-valley graphene model, we take…”

mentioning

confidence: 99%

“…( 71), (74), and (75) of Ref. [1] with |φ 0 | = π/2, and the T qj , S l 0 matrices have the same form as the T s,qj , S η s,0 matrices in Tab. I(a) with wm,µ = 0.…”

mentioning

confidence: 99%

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