Inverse Anderson localization in magic-angle twisted bilayer graphene-hBN quasicrystals

Quasiperiodicity in crystals corresponds to long range order with broken translational symmetry due to forbidden crystallographic tiling. In this work we study the electronic wavefunction of an effective quasiperiodic structure from overlapping two incommensurate moiré patterns  namely magic angle twisted bilayer graphene (MATBG) and twisted graphene-hBN. For regular bands, electrons perceive this quasiperiodicity as defects and corresponding scattering can generate a stronger electronic gap in the density of states forming an insulator. However, in the presence of flat bands in MATBG, theory predicts that the electrons, initially localized at the AA sites, can be delocalized by increasing disorder strength. We show using real-space imaging that as the kinetic energy of the electrons is increased, the localized electrons are exposed to the underlying quasicrystalline potential and undergo an inverse Anderson localization forming a fractal delocalized phase. This happens because the electrons experience the graphene-hBN remote bands with higher energy. We further map these remote bands from the density of states images to show the fractal nature of them due to quasiperiodicity. The localization-delocalization transition mediated by such quasiperiodic potential is a two-dimensional analogue of the Aubry-André model and is a unique platform to study the effects of quasiperiodicity in flat bands.