Observation of Van Hove singularities in twisted graphene layers

Electronic instabilities at the crossing of the Fermi energy with a Van Hove singularity1 in the density of states often lead to new phases of matter such as superconductivity2,3, magnetism4 or density waves5. 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 energy6 and hence difficult to reach with standard doping and gating techniques7. 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 tunnelling 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. In two dimensions, a saddle point in the electronic band structure leads to a divergence in the density of states, also known as a Van Hove singularity1 (VHS). When the Fermi energy (EF) is close to the VHS, interactions, however weak, are magnified by the enhanced density of states (DOS), resulting in instabilities, which can give rise to new phases of matter2–5 with desirable properties. This implies the possibility of engineering material properties by bringing EF and the VHS together. However, in most materials one cannot change the position of the VHS in the band structure. Instead, it may be possible to tune EF through the VHS by chemical doping8 or by gating7. In this regard, graphene, the recently discovered two-dimensional form of carbon, is quite special5,9. It has linearly dispersing bands at the K (K) point in the Brillouin zone, the so-called Dirac points, and a DOS that is linear and vanishes at Dirac point. The fact that this material is truly twodimensional and has a lowDOSmeans that it cannot screen applied electric fields, allowing for strong gating and ambipolar behaviour7. However, although the band structure of graphene5 contains a VHS, its large distance from the Dirac point makes it prohibitively difficult to reach by either gating or chemical doping. We show that by introducing a rotation between stacked graphene layers, it is possible to induceVHSs that arewithin the range ofEF achievable by gate tuning. As the samples studied here are not intentionally doped, EF is within a fewmillielectronvolts of the Dirac point. Rotation between graphene layers is often observed as a Moiré pattern on graphite surfaces10, as illustrated in Fig. 1. Graphite consists of stacked layers of graphene, the lattice structure of which contains two interpenetrating triangular sublattices, denoted A and B. In the most common (Bernal) stacking, adjacent layers