Moiré butterflies in twisted bilayer graphene

Bistritzer, Rafi; MacDonald, Allan H.

doi:10.1103/physrevb.84.035440

Cited by 221 publications

(222 citation statements)

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“…Although twisted bilayers with small rotation angles (typically 10 ) appear as a fascinating field of development for the physics of graphene [22,37,38], uncertainties about the mechanism of interlayer interaction remain [36,39]. Here we show that graphene layers rotated between 1 and 10 present singularities in the LDOS.…”

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confidence: 80%

“…In particular, recent scanning tunneling microscopy and spectroscopy (STM and STS) studies have demonstrated the renormalization of the band velocity [35] and the appearance of van Hove singularities in the local DOS (LDOS) [13] of three twisted layers configurations, one measured at the graphite surface and two on few layers graphene (FLG) grown on Ni. At variance, a careful angle resolved photoemission spectroscopy investigation of FLG on the SiC C face detected neither a van Hove singularity nor any significant change in the Fermi velocity in the range 1 < < 10 , and suggests major problems in our current understanding of twisted graphene layers [36].Although twisted bilayers with small rotation angles (typically 10 ) appear as a fascinating field of development for the physics of graphene [22,37,38], uncertainties about the mechanism of interlayer interaction remain [36,39]. Here we show that graphene layers rotated between 1 and 10 present singularities in the LDOS.…”

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confidence: 99%

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Unraveling the Intrinsic and Robust Nature of van Hove Singularities in Twisted Bilayer Graphene by Scanning Tunneling Microscopy and Theoretical Analysis

et al. 2012

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Extensive scanning tunneling microscopy and spectroscopy experiments complemented by firstprinciples and parametrized tight binding calculations provide a clear answer to the existence, origin, and robustness of van Hove singularities (vHs) in twisted graphene layers. Our results are conclusive: vHs due to interlayer coupling are ubiquitously present in a broad range (from 1 to 10 ) of rotation angles in our graphene on 6H-SiC(000-1) samples. From the variation of the energy separation of the vHs with the rotation angle we are able to recover the Fermi velocity of a graphene monolayer as well as the strength of the interlayer interaction. The robustness of the vHs is assessed both by experiments, which show that they survive in the presence of a third graphene layer, and by calculations, which test the role of the periodic modulation and absolute value of the interlayer distance. Finally, we clarify the role of the layer topographic corrugation and of electronic effects in the apparent moiré contrast measured on the STM images. DOI: 10.1103/PhysRevLett.109.196802 PACS numbers: 73.22.Pr, 61.48.Gh, 68.37.Ef, 73.20.At Soon after the discovery of the unique electronic properties of graphene [1-3], suggestions were made for engineering the band structure of this material. It has been proposed that periodic potentials with wavelengths in the nanometer range could lead to anisotropic renormalization of the velocity of low energy charge carriers [4] or to the generation of new massless Dirac fermions [5]. Experimental works intended for verifying these theoretical predictions were recently reported [6][7][8], where the periodic perturbation was generated either by a lattice mismatch with the supporting material or by a self-organized array of clusters. An alternative route for modifying graphene's band structure would be to exploit a rotation between stacked graphene layers [9]. According to calculations, for large angles ( !15 ) the low energy band structure of graphene should be preserved [10][11][12]. For intermediate angles (1 15 ), it is predicted that, while the linear dispersion persists in the vicinity of the Dirac points of both layers, the band velocity is depressed and two saddle points appear in the band structure, giving rise to two logarithmic van Hove singularities (vHs) in the density of states (DOS) [9,[13][14][15][16][17][18]. For smaller angles ( 1 ) weakly dispersive bands appear at low energy [19,20] with sharp DOS peaks very close to the Dirac point [17,18].Twisted graphene layers are commonly found on different substrates, such as metals [13,21,22], the C face of SiC [23][24][25], or graphite surfaces [26,27]. Transfer techniques yielding large domains of twisted bilayers over a macroscopic sample [28] and quantitative, fast, Raman characterization tools [29,30] have recently been proposed. However, despite the fact that rotated graphene layers are readily available and a number of measurements have confirmed that large twist angles lead to an electronic decoupling of stacked graphene layers [...

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Unraveling the Intrinsic and Robust Nature of van Hove Singularities in Twisted Bilayer Graphene by Scanning Tunneling Microscopy and Theoretical Analysis

et al. 2012

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“…We now turn to the magnetotransport properties of STA bilayer graphene. The energy spectrum of a 2D electron system subject to a spatially periodic potential, and a perpendicular magnetic field (B) has a fractal structure known as the Hofstadter butterfly, characterized by two topological integers: ν, representing the Hall conductivity in units of e 2 /h, and s, the index of subband filling (31)(32)(33)(34). Gaps in the energy spectrum are observed when the density per moiré unit cell and the magnetic flux per moiré unit cell (ϕ ≡ BA) satisfy the following Diophantine equation:…”

Section: Resultsmentioning

confidence: 99%

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Kim

DaSilva

Huang

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

541

408

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According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moiré patterns produced by small misalignments between its individual layer honeycomb lattices. We have realized bilayer graphene moiré crystals with accurately controlled twist angles smaller than 1°and studied their properties using scanning probe microscopy and electron transport. We observe conductivity minima at charge neutrality, satellite gaps that appear at anomalous carrier densities for twist angles smaller than 1°, and tunneling densities-of-states that are strongly dependent on carrier density. These features are robust up to large transverse electric fields. In perpendicular magnetic fields, we observe the emergence of a Hofstadter butterfly in the energy spectrum, with fourfold degenerate Landau levels, and broken symmetry quantum Hall states at filling factors ±1, 2, 3. These observations demonstrate that at small twist angles, the electronic properties of bilayer graphene moiré crystals are strongly altered by electron-electron interactions.moiré crystal | graphene | twisted bilayer | moiré band | Hofstadter butterfly M oiré patterns form when nearly identical two-dimensional (2D) crystals are overlaid with a small relative twist angle (1-4). The electronic properties of moiré crystals depend sensitively on the ratio of the interlayer hybridization strength, which is independent of twist angle, to the band energy shifts produced by momentum space rotation (5-12). In bilayer graphene, this ratio is small when twist angles exceed about 2°(10, 13), allowing moiré crystal electronic structure to be easily understood using perturbation theory (5). At smaller twist angles, electronic properties become increasingly complex. Theory (14, 15) has predicted that extremely flat bands appear at a series of magic angles, the largest of which is close to 1°. Flat bands in 2D electron systems, for example the Landau level bands that appear in the presence of external magnetic fields, allow for physical properties that are dominated by electron-electron interactions, and have been friendly territory for the discovery of fundamentally new states of matter. Here we report transport and scanning probe microscopy (SPM) studies of bilayer graphene moiré crystals with carefully controlled small-twist angles (STA), below 1°. We find that conductivity minima emerge in transport at neutrality, and at anomalous satellite densities that correspond to ±8 additional electrons in the moiré crystal unit cell, and that the conductivity minimum at neutrality is not weakened by a transverse electric field applied between the layers. Our observations can be explained only by strong electronic correlations. MethodsOur STA bilayer graphene samples are fabricated by sequential graphene and hexagonal boron-nitride (hBN) flake pick-up steps using a hemispherical handle substrate (16) that allows an individual flake to be detached from a substrate while leaving flakes in its immediate proximity intact. To...

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“…Here small differences in the orbitally quantized states in two weakly coherence-split bands produces an amplitude modulation of the Landau level spectrum with a period that greatly exceeds the coherence scale, and should be observable by magnetotransport in the weak field regime. Small rotations angles can introduce long spatial Moire periods for twisted bilayers that can be made commensurate with the magnetic length h/eB on accessible field scales, accessing Hofstadter commensuration physics in a new family of materials [34]. The band flattening theoretically predicted for in the small twist angle regime will surely focus attention on many body effects in the low energy physics.…”

Section: Discussionmentioning

confidence: 99%