Flat-bands in two stacked Penrose lattices

Strongly correlated phases in Moiré materials with flat bands in twisted systems, play the main role to explain the superconductivity in Twisted Bilayer Graphene. Decagonal quasicrystals are a type of quasicrystals that has quasiperiodic layers stacked periodically. The Penrose tessellation is the two dimensional most used model to study quasicrystals due to presenting the 5-fold symmetry and quasiperiodicity, as in quasicrystals. In this work, flat bands are found in quasicrystals after a translation and rotation, using the Tight Binding model. The quasicrystalline phases and confined electronic states rise from rotating two Penrose lattices, which are analysed in detail to understand the emergence of this bands.