Electronic structure and quantum transport in twisted bilayer graphene with resonant scatterers

Stacking layered materials revealed to be a very powerful method to tailor their electronic properties. It has indeed been theoretically and experimentally shown that twisted bilayers of graphene (tBLG) with a rotation angle $\ensuremath{\theta}$, forming a Moir\'e pattern, confine electrons in a tunable way as a function of $\ensuremath{\theta}$. Here, we study electronic structure and transport in tBLG using tight-binding numerical calculations in commensurate twisted bilayer structures and a pertubative continuous theory, which is valid for not-too-small angles ($\ensuremath{\theta}>\ensuremath{\sim}{2}^{\ensuremath{\circ}}$). These two approaches allow us to understand the effect of $\ensuremath{\theta}$ on the local density of states, the electron lifetime due to disorder, the DC conductivity, and the conductivity quantum correction due to multiple scattering effects. We distinguish the cases where disorder is equally distributed over two layers or only one layer. When only one layer is disordered, diffusion properties depend strongly on $\ensuremath{\theta}$, thus showing the effect of Moir\'e electronic localization at intermediate angles $\ensuremath{\theta}, \ensuremath{\sim}{2}^{\ensuremath{\circ}}<\ensuremath{\theta}<\ensuremath{\sim}{20}^{\ensuremath{\circ}}$.