Observation of flat bands in twisted bilayer graphene

Lisi, Simone; Lu, Xiaobo; Benschop, Tjerk; Jong, Tobias A. de; Stepanov, Petr; Duran, Jose R.; Margot, Florian; Cucchi, Irène; Cappelli, Edoardo; Hunter, A. T.; Tamai, Anna; Kandyba, Viktor; Giampietri, Alessio; Barinov, Alexei; Jobst, Johannes; Stalman, Vincent; Leeuwenhoek, Maarten; Watanabe, Kenji; Taniguchi, Takashi; Rademaker, Louk; Molen, Sense Jan van der; Allan, Milan P.; Efetov, Dmitri K.; Baumberger, F.

doi:10.1038/s41567-020-01041-x

Cited by 210 publications

(151 citation statements)

References 35 publications

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“…In all panels it is clearly visible that relaxation mechanisms tend to maximize the energy gaps at and, in particular, in the case of the magic angle θ = 1.08 • , the gap separating the FBs from the higher (lower) energy bands is about 26 meV (16 meV), consistent with the experiments [1,2,8,[10][11][12][13]. On the other hand, those gaps cannot be reproduced at all if no relaxation is allowed.…”

Section: Electronic Propertiessupporting

confidence: 79%

“…[9], whose bandwidth, of the order of ∼10 meV, has been confirmed also from tunnel spectroscopy experiments [8,[10][11][12]. The FBs' manifold, which can host up to four electrons above the Fermi energy and four holes below it, is separated by an energy gap of ∼50 meV from both higher and lower energy bands and has been clearly observed in recent nano-ARPES measurements [13]. When an external gate tunes the system chemical potential within these gaps, a clear band insulating phase appears.…”

Section: Introductionsupporting

confidence: 59%

“…The rotation is carried out starting from two perfectly AA stacked graphene layers and rotating around an axis orthogonal to the layers and passing through two C atoms, one on top of the other, belonging to the two planes (that therefore preserve their initial AA stacking). The respective structures can also be classified, according to the notation commonly used in the literature [55], using the pair of indexes (n, m): (31,30), (21,20), (13,12), and (9,8) Sampling of the Brillouin zone (BZ) for the self-consistent (SCF) calculations was restricted at the point for all four systems; no significant changes were observed after increasing the size of the sampling of the BZ for the smaller supercells. Single-particle energies at other points in the BZ were obtained by non-SCF calculations.…”

Section: Methodsmentioning

confidence: 99%

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Structural relaxation and low-energy properties of twisted bilayer graphene

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Conte

Cataudella

et al. 2020

Phys. Rev. Research

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The structural and electronic properties of twisted bilayer graphene are investigated from first-principles and tight-binding approach as a function of the twist angle (ranging from the first "magic" angle θ = 1.08 • to θ = 13.17 • , with the former corresponding to the largest unit cell, comprising 11,164 carbon atoms). By properly taking into account the long-range van der Waals (vdW) interaction, we provide the patterns for the atomic displacements (with respect to the ideal twisted bilayer). The out-of-plane relaxation shows an oscillating ("buckling") behavior, very evident for the smallest angles, with the atoms around the AA stacking regions interested by the largest displacements. The out-of-plane displacements are accompanied by a significant in-plane relaxation, showing a vortexlike pattern, where the vorticity (intended as curl of the displacement field) is reverted when moving from the top to the bottom plane and vice versa. Overall, the atomic relaxation results in the shrinking of the AA stacking regions in favor of the more energetically favorable AB/BA stacking domains. The measured flat bands emerging at the first magic angle can be accurately described only if the atomic relaxations are taken into account. Quite importantly, the experimental gaps separating the flat-band manifold from the higher and lower energy bands are intimately related to out-of-plane relaxations. The stability of the relaxed bilayer at the first magic angle is estimated to be of the order of 0.5-0.9 meV per atom (or 7-10 K). Our calculations shed light on the importance of an accurate description of the vdW interaction and of the resulting atomic relaxation to envisage the electronic structure of this really peculiar kind of vdW bilayers.

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Section: Electronic Propertiessupporting

confidence: 79%

Section: Introductionsupporting

confidence: 59%

Section: Methodsmentioning

confidence: 99%

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Structural relaxation and low-energy properties of twisted bilayer graphene

Cantele

Conte

Cataudella

et al. 2020

Phys. Rev. Research

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“…The energy‐ and momentum‐dependent evolution of the interlayer hybridization between the Dirac cones of twisted graphene layers has been observed in angle‐resolved photoemission spectroscopy (ARPES) experiments for large twists [ 28,29 ] and near the magic angle, [ 30,31 ] but the effect of gating in a functional device has not been previously explored. We achieve this by focusing a beam of 60 eV photons to a spot‐size of 690 nm using a Fresnel zone plate, leading to angle‐resolved photoemission with nanoscale spatial resolution (nanoARPES) from a twBLG flake supported on hexagonal boron nitride and back‐gated by graphite as sketched in Figure a.…”

Section: Figurementioning

confidence: 99%

“…We obtain

| G_{m} | = 0.63

Å −1 for our twist angle, which is roughly a factor of 11 times larger than the mini BZ corresponding to the “magic angle” of 1.1°. [ 4 ] In the latter case, the k ‐dependent linewidth of the features becomes comparable to the full size of the mini BZ, [ 30,31 ] making a detailed analysis of features within a single mini BZ almost impossible. Here we exploit the larger mini BZ presented in Figure 2b to track the evolution of the key features, which are the superlattice vHs and the mini gap Δ , and are able to spectrally resolve them within the mini BZ.…”

Section: Figurementioning

confidence: 99%

Observation of Electrically Tunable van Hove Singularities in Twisted Bilayer Graphene from NanoARPES

et al. 2020

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The possibility of triggering correlated phenomena by placing a singularity of the density of states near the Fermi energy remains an intriguing avenue toward engineering the properties of quantum materials. Twisted bilayer graphene is a key material in this regard because the superlattice produced by the rotated graphene layers introduces a van Hove singularity and flat bands near the Fermi energy that cause the emergence of numerous correlated phases, including superconductivity. Direct demonstration of electrostatic control of the superlattice bands over a wide energy range has, so far, been critically missing. This work examines the effect of electrical doping on the electronic band structure of twisted bilayer graphene using a back‐gated device architecture for angle‐resolved photoemission measurements with a nano‐focused light spot. A twist angle of 12.2° is selected such that the superlattice Brillouin zone is sufficiently large to enable identification of van Hove singularities and flat band segments in momentum space. The doping dependence of these features is extracted over an energy range of 0.4 eV, expanding the combinations of twist angle and doping where they can be placed at the Fermi energy and thereby induce new correlated electronic phases in twisted bilayer graphene.

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Polaritons in Van der Waals Heterostructures

et al. 2023

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Tunable nanophotonic systems that can be integrated with silicon and manipulate light at deep-subwavelength scales is of paramount importance for photonic integrated circuits, [1] enhanced light-matter interaction, [2] sub-diffraction imaging, [3] metamaterials, [4] and negative refraction [5] among other feats. In particular, polaritons in 2D materials exhibit the highest degree of mode confinement. [6] A variety of highly confined polaritons with unique properties [6,7] have been demonstrated in 2D materials, for example, electrically tunable plasmons in graphene, [7a,8] ultralow-loss phonon polaritons in hexagonal boron nitride (h-BN) [9] and α-MoO 3 , [7c,7d] room-temperature exciton polaritons in MoSe 2 , [10] WSe 2 [11] and CsPbBr 3 microsheets, [12] and Cooper-pair polaritons. [13] These surface modes have prompted the exploration of multiple potential applications, such as surface-enhanced infrared spectroscopy, [8a,14] optical sensors, [15] nanolasers, [16] light modulators, [17] and nanophotonic circuits. [18] However, in most practical applications, important challenges, such as relatively large optical losses, reduced operation frequency range, and slow modulation speed, are remaining.The hybrid light-matter nature of polaritons (i.e., quasiparticles made up of a photons coupled to polarization charges in a material) can be passively tuned by designing the composition and geometry of the hosting materials, [9,19] offering important advantages for nanophotonic systems. [6a,20] Recently, van der Waals heterostructures (vdWHs), which can be fabricated by exfoliating 2D materials down to isolated monolayers and subsequently reassembling them in a layer by layer fashion in precisely chosen compositions, stacking sequence, and twist angles, provide a versatile way to customize polaritons. [21] For example, an ultralong lifetime graphene plasmon in graphene/h-BN vdWHs, [7a,22] an efficient all-optical modulation of graphene plasmons in the graphene/ monolayer MoS 2 vdWHs, [23] a strong plasmonic nonlinear response in graphene/metal heterostructures [24] have been demonstrated. Moreover, the behavior of polaritons can also be modulated by creating moiré patterns in the vdWHs, such that one can obtain, for example, an extremely long plasmon lifetime (≈3 ps) in stacked bilayer graphene, [25] photonic crystals of twisted bilayer graphene (TBLG), [26] and tunable topological transitions of phonon polaritons in twisted α-MoO 3 bilayers. [27] 2D monolayers supporting a wide variety of highly confined plasmons, phonon polaritons, and exciton polaritons can be vertically stacked in van der Waals heterostructures (vdWHs) with controlled constituent layers, stacking sequence, and even twist angles. vdWHs combine advantages of 2D material polaritons, rich optical structure design, and atomic scale integration, which have greatly extended the performance and functions of polaritons, such as wide frequency range, long lifetime, ultrafast all-optical modulation, and photonic crystals for nanoscale light. Here, th...

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Observation of flat bands in twisted bilayer graphene

Cited by 210 publications

References 35 publications

Structural relaxation and low-energy properties of twisted bilayer graphene

Structural relaxation and low-energy properties of twisted bilayer graphene

Observation of Electrically Tunable van Hove Singularities in Twisted Bilayer Graphene from NanoARPES

Polaritons in Van der Waals Heterostructures

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