Spatially resolved electronic structure of twisted graphene

Abstract

We have used scanning tunneling microscopy and spectroscopy to resolve the spatial variation of the density of states of twisted graphene layers on top of a highly oriented pyrolytic graphite substrate. Owing to the twist a moire pattern develops with a periodicity that is substantially larger than the periodicity of a single layer graphene. The twisted graphene layer has electronic properties that are distinctly different from that of a single layer graphene due to the nonzero interlayer coupling. For small twist angles (about 1-3.5 degree) the integrated differential conductivity spectrum exhibits two well-defined Van Hove singularities. Spatial maps of the differential conductivity that are recorded at energies near the Fermi level exhibit a honeycomb structure that is comprised of two inequivalent hexagonal sub-lattices. For energies |E-E_F|>0.3 eV the hexagonal structure in the differential conductivity maps vanishes. We have performed tight-binding calculations of the twisted graphene system using the propagation method, in which a third graphene layer is added to mimic the substrate. This third layer lowers the symmetry and explains the development of the two hexagonal sub-lattices in the moire pattern. Our experimental results are in excellent agreement with the tight-binding calculations.Comment: To appear in Phys. Rev.

Scanning tunneling microscopy and spectroscopy of twisted trilayer graphene

“…shown in the STM image (Fig. 3(c)), in consistent with that observed in TBG in previous works 1,16,21,22 . This result indicates the presence of the moiré potential in the TTG due to the twist-induced moiré pattern, which is similar as that observed in the TBG.…”

“…3(d)) reveals the same period and circular symmetry of the moiré pattern but exhibits the inverted contrast comparing with that shown in the STM image ( Fig. 3(c)), in consistent with that observed in TBG in previous works 1,16,21,22 . This result indicates the presence of the moiré potential in the TTG due to the twist-induced moiré pattern, which is similar as that observed in the Figure S10) 38 .…”

Helical network model for twisted bilayer graphene

“…Whereas an engineering of a network of helical states with tunable geometry is a challenging problem, the triangular one has been recently observed [20] with help of scanning tunneling spectroscopy (STM) in misoriented graphene bilayers [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. In the presence of a twist local stacking arrangement changes slowly in space in a periodic moiré pattern in which regions with approximate AB and BA stacking are separated by domain walls with helical states .…”

Singularities and topologically protected states in twisted bilayer graphene

“…The peaks, which are referred to as Van Hove singularities (VHs), arise due to the hybridization of the Dirac cones of the top and bottom graphene layer. 22 Using the continuum approximation for a bilayer graphene with a small twist angle, the energy gap of the two Van Hove singularities is given by DE VHs ¼ 2 hv F Ksinðh=2Þ À 2t ? , where v F is the Fermi velocity of the twisted graphene bilayer andt ?…”