Van Hove singularities in doped twisted graphene bilayers studied by scanning tunneling spectroscopy

Twisted bilayers (tBL) form a class of graphene based material whose low energy electronic structure can be controlled by a geometric parameter, namely by the rotation angle  between the graphene layers. For undoped (neutral) systems, this property has been established by a number of theoretical [1,2] and experimental studies [3,4]. For large angles (>10°), the layers are electronically decoupled and the low energy band structure looks like a simple superposition of the Dirac cones of the individual graphene planes. For smaller angles, a pair of logarithmic divergences in the density of states (DOS) called van Hove singularities (vHs), related to a saddle point in the band structure, develop within 1 eV from the Fermi level [2-4]. Their energies are almost symmetric with respect to the Dirac point and decrease with . For even smaller angles (<1-2°), flat bands appear at low energy [2], the vHs tend to localize in AA stacked areas [2,3] and additional low energy DOS features related to confinement appear [2]. The twist induced changes in the band structure should be reflected in the physical properties of the bilayers. A rich physics is anticipated in magnetotransport experiments provided the Fermi level EF can be brought in the vicinity or above the vHs [5], although it has not yet been revealed by the experiments reported so far. Structures in the optical conductivity induced by the presence of the vHs have been reported in a wide energy range depending on the value of  [6]. Calculations moreover predict that doping could markedly influence the optical properties when EF reaches the vHs [7]. Owing to the variety of original properties expected upon doping, it is important to determine in a direct way the influence of this parameter on the low energy electronic structure of the twisted graphene layers. This is especially interesting for the doping levels which are accessible using a backgate, typically a few 10 12 cm -2 , to determine for instance at which angle one vHs crosses EF for a given charge. This would additionally allow the experimental investigation of the many body instabilities expected in this configuration [8].