Electronic instabilities at the crossing of the Fermi energy with a Van Hove singularity in the density of states often lead to new phases of matter such as superconductivity, magnetism or density waves. However, in most materials this condition is difficult to control. In the case of single-layer graphene, the singularity is too far from the Fermi energy and hence difficult to reach with standard doping and gating techniques. Here we report the observation of low-energy Van Hove singularities in twisted graphene layers seen as two pronounced peaks in the density of states measured by scanning tunneling spectroscopy. We demonstrate that a rotation between stacked graphene layers can generate Van Hove singularities, which can be brought arbitrarily close to the Fermi energy by varying the angle of rotation. This opens intriguing prospects for Van Hove singularity engineering of electronic phases.Comment: 21 pages 5 figure

In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers' two-dimensional and relativistic character. The first experimental evidence of the two-dimensional nature of graphene came from the observation of a sequence of plateaus in measurements of its transport properties in the presence of an applied magnetic field. These are signatures of the so-called integer quantum Hall effect. However, as a consequence of the relativistic character of the charge carriers, the integer quantum Hall effect observed in graphene is qualitatively different from its semiconductor analogue. As a third distinguishing feature of graphene, it has been conjectured that interactions and correlations should be important in this material, but surprisingly, evidence of collective behaviour in graphene is lacking. In particular, the quintessential collective quantum behaviour in two dimensions, the fractional quantum Hall effect (FQHE), has so far resisted observation in graphene despite intense efforts and theoretical predictions of its existence. Here we report the observation of the FQHE in graphene. Our observations are made possible by using suspended graphene devices probed by two-terminal charge transport measurements. This allows us to isolate the sample from substrate-induced perturbations that usually obscure the effects of interactions in this system and to avoid effects of finite geometry. At low carrier density, we find a field-induced transition to an insulator that competes with the FQHE, allowing its observation only in the highest quality samples. We believe that these results will open the door to the physics of FQHE and other collective behaviour in graphene.

We report high magnetic field scanning tunneling microscopy and Landau level spectroscopy of twisted graphene layers grown by chemical vapor deposition. For twist angles exceeding ~3° the low energy carriers exhibit Landau level spectra characteristic of massless Dirac fermions. Above 20° the layers effectively decouple and the electronic properties are indistinguishable from those in single-layer graphene, while for smaller angles we observe a slowdown of the carrier velocity which is strongly angle dependent. At the smallest angles the spectra are dominated by twist-induced van Hove singularities and the Dirac fermions eventually become localized. An unexpected electron-hole asymmetry is observed which is substantially larger than the asymmetry in either single or untwisted bilayer graphene.

We report low temperature high magnetic field scanning tunneling microscopy and spectroscopy of graphene flakes on graphite that exhibit the structural and electronic properties of graphene decoupled from the substrate.Pronounced peaks in the tunneling spectra develop with field revealing a Landau level sequence that provides a direct way to identify graphene and to determine the degree of its coupling to the substrate. The Fermi velocity and quasiparticle lifetime, obtained from the positions and width of the peaks, provide access to the electron-phonon and electron-electron interactions.

Scanning tunneling microscopy and spectroscopy in magnetic field was used to study Landau quantization in graphene and its dependence on charge carrier density. Measurements were carried out on exfoliated graphene samples deposited on a chlorinated SiO 2 thermal oxide which allowed observing the Landau level sequences characteristic of single layer graphene while tuning the density through the Si backgate. Upon changing the carrier density we find abrupt jumps in the Fermi level after each Landau level is filled. Moreover, the Landau level spacing shows a marked increase at low doping levels, consistent with an interaction-induced renormalization of the Dirac cone. One of the hallmarks of the relativistic charge carriers 1,2 in graphene is the appearance in a magnetic field of an unusual Landau level (LL) at zero energy which reflects the chiral symmetry of the low lying excitations. The presence of this LL has been inferred in magnetotransport measurements employing the standard configuration of graphene supported on SiO 2 3,4 from the conspicuous absence of a quantum Hall plateau at zero filling-factor. Remarkably because in graphene the carriers reside right at the surface, the LLs (including the LL at zero-energy) can be accessed directly through scanning tunneling spectroscopy (STS) as was demonstrated in studies of graphene samples supported on the surface of graphite 5,6 .However, the LLs were not observed in STS measurements on graphene samples supported on insulating substrates which allow control of the carrier density through gating. This is because due to the purely two dimensional nature of graphene, substrate induced potential fluctuations obscure the intrinsic physics of the charge carriers close to the Dirac point.One way to overcome this limitation is to use suspended samples 7,8 where transport measurements have shown that in the absence of the substrate the intrinsic Dirac point physics including interaction effects is revealed 9,10 . The use of suspended samples is however limited due to their fragility, small size and reduced range of gating. Finding a minimally invasive insulating substrate on which graphene can be gated and also visualized is therefore of great interest.By using scanning tunneling microscopy (STM) and spectroscopy (STS) we show that for graphene supported on SiO 2 substrates which were treated by chlorination to minimize trapped charges and in sufficiently large magnetic fields, the LL sequence specific to single layer graphene and its dependence on carrier density can be accessed. Upon varying the carrier-density sudden jumps of the Fermi-energy are observed after filling each LL. Moreover the measured density-dependence of the LL spacing shows a rapid increase upon approaching the Dirac-point, consistent with an interaction-induced renormalization of the Dirac cone.A simple method for preparing high quality graphene samples is mechanical exfoliation from graphite followed by deposition on the surface of SiO 2 capping a Si crystal 3 . This relative ease of samp...