Quasicrystals in Twisted Graphene on Hexagonal Boron Nitride viewed through Scanning Tunneling Microscopy and Spectroscopy

Twisted bilayer graphene (TBG) hosts moiré patterns with C3 rotational symmetry and a twist-angle dependent super-period. Aligning TBG with hexagonal Boron Nitride (hBN) breaks the C3 symmetry and introduces a new set of moiré patterns between the hBN and the adjacent graphene layer, GBN, that coexists with the TBG moiré pattern. Commensurate TBG and GBN moiré patterns which are known to produce non-trivial band topology giving rise to an anomalous quantum Hall effect, are difficult to realize as they require very precise alignment of the layers. Surprisingly, we find that commensurate TBG/GBN exist over a much wider than expected range of twist angles, indicating a strong tendency of the lattices to relax toward a commensurate state. In most cases however the two patterns are incommensurate resulting in a quasicrystal structure. Using scanning tunneling microscopy and spectroscopy we image the coexisting TBG/GBN moiré patterns simultaneously and study their electronic properties with spatially resolved local Density of States. We find that as a function of energy and magnetic field, the electronic states transit between crystal and quasicrystal structures. The latter exhibit unexpected symmetries and new periodicity emerging from the two sets of coexistent moiré patterns. Furthermore, the quasicrystal structures are accompanied by an unexpected emergence of flat electronic bands that reveal correlation induced gaps as the Fermi energy is swept through them.