Flat bands in twisted double bilayer graphene

Chebrolu, Narasimha Raju; Chittari, Bheema Lingam; Jung, Jeil

doi:10.1103/physrevb.99.235417

Cited by 193 publications

(193 citation statements)

References 58 publications

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“…The bandwidth has a clear trend of increasing with the electric field. This reasonably agrees with the results discussed in N. R. Chebrolu et al [19]. The bandwidth has a typical value ∼ 1 − 15 meV for mid-range of the electric field where the halo features appear on the electron side.…”

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Tunable bandwidths and gaps in twisted double bilayer graphene on the verge of correlations

et al. 2020

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We use temperature-dependent resistivity in small-angle twisted double bilayer graphene to measure bandwidths and gaps of the bands. This electron-hole asymmetric system has one set of non-dispersing bands that splits into two flat bands with the electric field -distinct from the twisted bilayer system. With electric field, the gap between two emergent flat bands increases monotonically and bandwidth is tuned from 1 meV to 15 meV. These two flat bands with gap result in a series of thermally induced insulator to metal transitions -we use a model, at charge neutrality, to measure the bandwidth using only transport measurements. Having two flat bands with tunable gap and bandwidth offers an opportunity to probe the emergence of correlations. arXiv:2001.09916v1 [cond-mat.mes-hall]

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confidence: 93%

“…The origin of the electric field tunability of the bandwidth is subject of detail theoretical and numerical calculation [19]. However, a simple picture is depicted in the inset of Fig.…”

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Tunable bandwidths and gaps in twisted double bilayer graphene on the verge of correlations

et al. 2020

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“…Our results demonstrate that these crystal fields will be generically relevant for the low energy dispersion of any van-der-Waals heterostructure with more than 3 layers or an asymmetric vertical arrangement of layers. Combining the experimentally measured band gap and our low energy description, we highlight that crystal fields will also substantially modify the electronic structure at generic twist-angles, and in particular in small-angle twisted double bilayer graphene [15][16][17]. As a result, our work suggests the importance of considering crystal field contributions to faithfully capture the low energy electronic band structure of small-angle twisted double bilayers, where superconductivity and strongly correlated behavior has been reported recently [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Gap Opening in Twisted Double Bilayer Graphene by Crystal Fields

et al. 2019

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Crystal fields occur due to a potential difference between chemically different atomic species. In Van-der-Waals heterostructures such fields are naturally present perpendicular to the planes. It has been realized recently that twisted graphene multilayers provide powerful playgrounds to engineer electronic properties by the number of layers, the twist angle, applied electric biases, electronic interactions and elastic relaxations, but crystal fields have not received the attention they deserve.Here we show that the bandstructure of large-angle twisted double bilayer graphene is strongly modified by crystal fields. In particular, we experimentally demonstrate that twisted double bilayer graphene, encapsulated between hBN layers, exhibits an intrinsic bandgap. By the application of an external field, the gaps in the individual bilayers can be closed, allowing to determine the crystal fields. We find that crystal fields point from the outer to the inner layers with strengths in the bottom/top bilayer E b = 0.13 V/nm ≈ −Et = 0.12 V/nm. We show both by means of first principles calculations and low energy models that crystal fields open a band gap in the groundstate. Our results put forward a physical scenario in which a crystal field effect in carbon substantially impacts the low energy properties of twisted double bilayer graphene, suggesting that such contributions must be taken into account in other regimes to faithfully predict the electronic properties of twisted graphene multilayers. arXiv:1910.10524v2 [cond-mat.mes-hall] 4 Nov 2019 a c FIG. 1. a) Two twisted, AB-stacked bilayer graphene (BG) sheets. The electrostatic potential of the outer layers is different from the potential in the inner layers. This leads to crystal fields Et = −E b pointing in opposite direction in the top and bottom BG. In the experiment, the two bilayer systems are encapsulated in hBN which reduces the strength of the crystal fields compared to vacuum. b) The TDBG band structure consists of Brillouin-zones of the top and bottom BG rotated with respect to each other. For large twist angles θ, the bands of the top and bottom layer intersect at energies large compared to the Fermi energies of the individual layers. Therefore, at typical Fermi energies, the individual BG band structures remain intact.The crystal fields open a single-particle gap in both layers. c) In such a structure we observe a gap at zero density and zero external field in a resistance versus density trace R(ntot). We show traces for two devices, device 1 is further discussed in the main text and further measurements of device 2 and device 3 are shown in the Supplemental Material.

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“…The non-monotonic behavior of the SiC/SiC valence band W and lack of electron-hole symmetry (not shown) can be traced to the unequal ω i values for the interlayer tunneling parameters. twisted bilayer graphene [69] and for the first magic angle corresponding to m = 1 in the minimal model of twisted bibilayer graphene [64] confirming that the magic twist angles should increase together with interlayer coupling strength as expected from this scaling relation [41,69]. These magic angles were defined as the θ values that give rise to bandwidth local minima rather than the angles where the effective Fermi velocity vanishes at the K-points of the mBZ [31] since this definition would become ambiguous in twisted bi-bilayers or gapped Dirac materials whose band edges already have zero Fermi velocity.…”

Section: Bandwidth Phase Diagram In Twisted Gapped Dirac Materialsmentioning

confidence: 99%

“…The Hamiltonian parameters for G/G systems are from Refs [69]. for rigid and Ref [64]. for out of plane relaxed geometries.…”

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Topological flat bands without magic angles in massive twisted bilayer graphenes

2020

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Twisted bilayer graphene (TBG) hosts nearly flat bands with narrow bandwidths of a few meV at certain magic twist angles. Here we show that in twisted gapped Dirac material bilayers, or massive twisted bilayer graphenes (MTBG), isolated nearly flat bands below a threshold bandwidth W c are expected for continuous small twist angles up to a critical θ c depending on the flatness of the original bands and the interlayer coupling strength. Narrow bandwidths of W 30 meV are expected for θ 3 • for twisted Dirac materials with intrinsic gaps of ∼ 2 eV that finds realization in monolayers of gapped transition metal dichalcogenides (TMDC), silicon carbide (SiC) among others, and even narrower bandwidths in hexagonal boron nitride (BN) whose gaps are ∼ 5 eV, while twisted graphene systems with smaller gaps of a few tens of meV, e.g. due to alignment with hexagonal boron nitride, show vestiges of the magic angles behavior in the bandwidth evolution. The phase diagram of finite valley Chern numbers of the isolated moire bands expands with increasing difference between the sublattice selective interlayer tunneling parameters. The valley contrasting circular dichroism for interband optical transitions is constructive near 0 • and destructive near 60 • alignments and can be tuned through electric field and gate driven polarization of the mini-valleys. Combining massive Dirac materials with various intrinsic gaps, Fermi velocities, interlayer tunneling strengths suggests optimistic prospects of increasing θ c and achieving correlated states with large U/W effective interaction versus bandwidth ratios.

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Flat bands in twisted double bilayer graphene

Cited by 193 publications

References 58 publications

Tunable bandwidths and gaps in twisted double bilayer graphene on the verge of correlations

Tunable bandwidths and gaps in twisted double bilayer graphene on the verge of correlations

Gap Opening in Twisted Double Bilayer Graphene by Crystal Fields

Topological flat bands without magic angles in massive twisted bilayer graphenes

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