Flat bands and gaps in twisted double bilayer graphene

Culchac, F. J.; Grande, Rafael; Capaz, Rodrigo B.; Chico, Leonor; Morell, E. Suárez

doi:10.1039/c9nr10830k

Cited by 55 publications

(40 citation statements)

References 50 publications

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“…As a reference, for twisted graphene multilayers t ≈ 3 eV and t ⊥ ≈ 0.15t. 1 Similar real-space models were used to study a variety of twisted graphene multilayers [10,36,50,51], providing a simple formalism to study the effect of dopants and impurities [52,53]. However, in contrast to continuum models [9,42,54], measuring of valley-related quantities with a real-space-based formalism is nontrivial.…”

Section: Electronic Structure Of Twisted Trilayer Graphenementioning

confidence: 99%

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

López-Bezanilla

Lado

2020

Phys. Rev. Research

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Twisted graphene multilayers have been demonstrated to yield a versatile playground to engineer controllable electronic states. Here, by combining first-principles calculations and low-energy models, we demonstrate that twisted graphene trilayers provide a tunable system where Van Hove singularities can be controlled electrically. In particular, it is shown that besides the band flattening, bulk valley currents appear, which can be quenched by local chemical dopants. We finally show that in the presence of electronic interactions, a nonuniform superfluid density emerges whose nonuniformity gives rise to spectroscopic signatures in dispersive higher-energy bands. Our results put forward twisted trilayers as a tunable van der Waals heterostructure displaying electrically controllable flat bands and bulk valley currents.

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Section: Electronic Structure Of Twisted Trilayer Graphenementioning

confidence: 99%

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

López-Bezanilla

Lado

2020

Phys. Rev. Research

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“…Especially, the stacking angle (θ°) control of BLG arises as an important research subject, as it shows unique physical properties depending on θ°6 , 7 . For example, superconductivity is observed from BLG having 1.1 o -twisted stacking angle [8][9][10] , θ°-tunable photoluminescence 11 , and θ°-dependent van Hove singularity 12,13 . For the successful and systematic studies of the correlation between the stacking angle of BLG and the above-mentioned properties, it is highly required to control the stacking angle of BLG, ideally upon its synthesis.…”

Section: Introductionmentioning

confidence: 99%

Specific stacking angles of bilayer graphene grown on atomic-flat and -stepped Cu surfaces

Cho¹,

Park²,

Kim³

et al. 2020

npj 2D Mater Appl

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Bilayer graphene (BLG) exhibits unique properties depending on a stacking angle between the two layers of graphene. Although it has been known that BLGs having stacking angles of 0° and 30° can be obtained by chemical vapor deposition (CVD), not much is known yet about the effect of copper (Cu) surface on the decision of stacking angle, through which further fine control of the stacking angle could be possible. Here, we report that the crystal plane of Cu catalyst plays a critical role in the selection of the stacking angle of BLG, and provide experimental and computational evidence that an atomic-flat Cu (111) surface generates BLGs having 0° and 30° of stacking angle, while atomic-stepped Cu (311) and Cu (110) surfaces mainly produce small stacking angle BLGs with 3–5° of stacking angle as a major product by CVD.

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“…In fact, it has been discovered that at certain, so-called magic angles, flat energy bands occur which then give rise to a plethora of highly correlated phases. An exciting example is a superconducting phase that occurs at the first magic twist angle [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. This superconducting state was first discovered in a land-mark paper in Nature Physics [20].…”

Section: Introductionmentioning

confidence: 99%

Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene

Benlakhouy,

Jellal,

Bahlouli

et al. 2021

Preprint

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We study the magnetic field induced Hofstadter butterfly in twisted bilayer graphene (TBG) in various kinds of situations. First, we study the equilibrium case and identify the interlayer hopping processes that are most crucial for the appearance of a Hofstadter butterfly. Surprisingly, the hopping processes that are important for the appearance of the Hofstadter butterfly can be categorized as AA stacking type -that is interlayer hoppings between equivalent sublattices. This is in contrast to AB/BA-type hoppings that are important for the appearance of flat bands in magic angle TBG and were discussed in [1]. We also find that if AB-type interlayer-hopping processes are turned off the resulting model is chiral but differs from the model discussed in [1]. Therefore, TBG has two separate chiral limits -one of them is important to understand the formation of flat bands and the other for the Hofstadter butterfly. Taking this as motivation we discuss how the role of AA-type hoppings in combination with lattice relaxation effects can make individual Landau levels slightly harder to resolve in an experimental setting than one would expect from a non-relaxed lattice setting. Finally, we consider the impact of different forms of light on the fractal structure of the butterfly. Particularly, we study the impact of circularly polarized light and longitudinal light originating from a waveguide. As the system is exposed to circularly polarized light we find butterflies with increasingly pronounced asymmetry with respect to energy E = 0. This is due to the introduction of a gap term that breaks the chiral symmetries for both of the two chiral limits mentioned above. Lastly, we study the effect of longitudinal light that can be produced at the exit of a waveguide. Here, we find that no additional terms that break chiral symmetry are introduced. Therefore, it is found to lead to no increase in asymmetry of the energy spectrum. In fact, we identify specific experimentally accessible driving regimes in which the TBG achieves any of the two chiral limits.

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Flat bands and gaps in twisted double bilayer graphene

Cited by 55 publications

References 50 publications

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

Specific stacking angles of bilayer graphene grown on atomic-flat and -stepped Cu surfaces

Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene

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