Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals

In this review, we present recent works on materials whose common point is the presence of electronic bands of very low dispersion, called "flat bands", which are due to specific atomic order effects without electron interactions. These states are always indicative of some form of confinement and have consequences on the electronic properties. A first part is devoted to the cases where this confinement is due to the long-range geometry of the defect-free structure. We have thus studied periodic approximant structures of quasiperiodic Penrose and octagonal tilings, and twisted bilayers of graphene (TBG) or transition metal dichalcogenides (TMDs) whose rotation angle between the two layers assumes a special value, called "magic angle". In these materials, the flat bands correspond to electronic states distributed over a very large number of atoms (several hundreds or even thousands of atoms). We have shown that their electronic transport properties cannot be described by usual Bloch-Boltzmann theories, because the interband terms of the velocity operator dominate the intraband terms as far as quantum diffusion is concerned. In the case of TBG, flat bands can induce a magnetic state and other electron-electron correlation effects. The second part focuses on two-dimensional nanomaterials in the presence of local point defects that cause resonant electronic states (vacancies, adsorbed atoms or molecules). We present studies on monolayer graphene, twisted or Bernal bilayer graphene, carbon nanotubes, monolayer and multilayer black phosphorene, and monolayer TMDs. A recent result is the discovery that the selective functionalization of a Bernal bilayer graphene sublattice leads to a metallic or insulating behavior depending on the functionalized sublattice type. This result suggests that functionalization can be a key parameter to control the electronic properties of 2D materials.