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

Abstract

The effect of electron doping on the van Hove singularities (vHs) which develop in twisted graphene bilayers (tBLs) is studied for a broad range of rotation angles $\ensuremath{\theta}\phantom{\rule{0.28em}{0ex}}(1.{5}^{\ensuremath{\circ}}<\ensuremath{\theta}<{15}^{\ensuremath{\circ}})$ by means of scanning tunneling microscopy and spectroscopy. Bilayer and trilayer graphene islands were grown on the 6H-SiC(000-1) $(3\ifmmode\times\else\texttimes\fi{}3)$ surface, which results in tBLs doped in the ${10}^{12}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ range by charge transfer from the substrate. For large angles, doping manifests in a strong asymmetry of the positions of the upper (in empty states) and lower (in occupied states) vHs with respect to the Fermi level. The splitting of these vHs energies is found essentially independent of doping for the whole range of $\ensuremath{\theta}$ values, but the center of theses vHs shifts towards negative energies with increasing electron doping. Consequently, the upper vHs crosses the Fermi level for smaller angles (around ${3}^{\ensuremath{\circ}}$). The analysis of the data performed using tight-binding calculations and simple electrostatic considerations shows that the interlayer bias remains small $(<100\phantom{\rule{0.28em}{0ex}}\mathrm{mV})$ for the doping level resulting from the interfacial charge transfer $(\ensuremath{\simeq}5\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2})$.