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

Abstract

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 [...

Many‐body effects in optical response of graphene‐based structures

“…These singularities were identified as the peaks appeared symmetrically with respect to the Fermi level in scanning tunneling spectra of twisted bilayers for rotation angles between 1 and 108. [86,87] The features of the lowenergy band structure can be understood by considering the Brillouin zones of superposed layers. As a result of rotation, the Dirac cones originating from individual layers separate and their intersection at a higher energy produces the two saddle points (Fig.…”

Observation of the intrinsic bandgap behaviour in as-grown epitaxial twisted graphene

“…A full-tight binding calculation showed a reduction of the Fermi velocity due to interlayer interaction 2 . For TG with small twist angles (yo15°), the experimental studies showed 1,3,6,9 that the Dirac cones for each layer persist but van Hove singularities are present due to the interlayer interaction. For large twist angles, the twisted layers effectively de-couple from each other and become indistinguishable from SLG 7 .…”

“…T he rotational stacking of graphene layers alters their electronic characteristics resulting in novel and rich physics [1][2][3][4][5][6][7][8] . Bernal (AB)-stacked graphene rotated by 60°b etween adjacent layers is well understood and its electronic properties are radically different from single-layer graphene (SLG).…”

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

“…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)(6)(7)(8)(9)(10)(11)(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).…”