Slightly misoriented surface graphene layer on highly ordered pyrolytic graphite (HOPG) can result in Moiré patterns (MP). Two van Hove singularity (VHS) peaks in the density of states are observed with scanning tunneling spectroscopy on a series of the MPs with different periods on HOPG surface, flanking the Fermi energy. The energy difference between the two VHS peaks (ΔEVHS) is linearly proportional to the sine of interlayer rotation angle. A similar relation between ΔEVHS and MP periods has recently been reported on twisted graphene layers. Compared to the case of twisted graphene layers, the Fermi velocity of MPs on a HOPG surface is found to be larger, and the interlayer hopping is enhanced.
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Zhang et al. (2013) studied this question.