The presence of flat bands near Fermi level has been proposed as an explanation for high transition temperature superconductors. The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this Rapid Communication, we found nondispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion of bilayer graphene to the characteristic linear dispersion of graphene. This transition occurs for relative rotation angles of layers around 1.5\ifmmode^\circ\else\textdegree\fi{} and is related to a process of layer decoupling. We have performed ab initio calculations to develop a tight-binding model with an interaction Hamiltonian between layers that include the $\pi${} orbitals of all atoms and takes into account interactions up to third nearest neighbors within a layer.

We use density-functional theory calculations to study the stability, electronic, and optical properties of free-base and Zn porphyrins and phthalocyanines (H2P, H2Pc, ZnP, and ZnPc) noncovalently attached onto a semiconducting carbon nanotube (CNT). The macrocycle physisorption is described by van der Waals density functional while optical response is obtained through the imaginary part of the dielectric function. Our results show a rather strong macrocycle binding energy, ranging from 1.0 to 1.5 eV, whereas the CNT geometry and electronic properties are weakly affected by the adsorbates. The optical spectrum shows that CNT-porphyrins and CNT-phthalocyanines assemblies would absorb at different energies of the visible solar radiation spectrum, which would increase the conversion energy efficiency in a photovoltaic device including both macrocycles.