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A periodic spatial modulation, as created by a moir\'e pattern, has beenextensively studied with the view to engineer and tune the properties ofgraphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightlymisaligned with the top and bottom hBN layers experiences two interferingmoir\'e patterns, resulting in a so-called super-moir\'e (SM). This leads to alattice and electronic spectrum reconstruction. A geometrical construction ofthe non-relaxed SM patterns allows us to indicate qualitatively the inducedchanges in the electronic properties and to locate the SM features in thedensity of states and in the conductivity. To emphasize the effect of latticerelaxation, we report band gaps at all Dirac-like points in the hole doped partof the reconstructed spectrum, which are expected to be enhanced when includinginteraction effects. Our result is able to distinguish effects due to latticerelaxation and due to the interfering SM and provides a clear picture on theorigin of recently experimentally observed effects in such trilayerheterostuctures.

Double moir\'e with a twist: super-moir\'e in encapsulated graphene