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 report on the effects of laser illumination on the electronic properties of bilayer graphene. By using Floquet theory combined with Green's functions, we unveil the appearance of laser-induced gaps not only at integer multiples of $\hbar${}$\Omega${}/2 but also at the Dirac point with features which are shown to depend strongly on the laser polarization. Trigonal warping corrections are shown to lead to important corrections for radiation in the terahertz range, reducing the size of the dynamical gaps. Furthermore, our analysis of the topological properties at low energies reveals that, when irradiated with linearly polarized light, ideal bilayer graphene behaves as a trivial insulator, whereas circular polarization leads to a nontrivial insulator per valley.

We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer graphene spectrum shows two parabolic Bernal-like bands and a twistedlike Dirac cone. For small twist angles, the parabolic bands present a gap that increases for decreasing rotation angle. There is also a shift in the twistedlike Dirac cone with a similar angle dependence. We correlate the gap in the trilayer with the shift of the Dirac cone in an isolated twisted bilayer, which is due to the loss of electron-hole symmetry caused by sublattice mixing in the rotated geometry. Using a tight-binding and a continuum model, we derive an effective Hamiltonian which accounts for the relevant low-energy properties of this system.

Recently intrinsic ferromagnetism in two-dimensional(2D) van der Waals materials was discovered (Huang et al 2017 Nature 546 270–3; Gong et al 2017 Nature 546 265–9; O’Hara et al 2018 Nano Lett . 18 3125–31). A monolayer of Chromiun triiodide(CrI ₃ ) is ferromagnetic while a bilayer structure was reported to be anti-ferromagnetic, moreover an external electric field changes its magnetic phase (Jiang et al 2018 Nat. Mater . 17 406–10). We have studied the two found in nature stackings of CrI ₃ bilayers and found that indeed the magnetic phase of one of them can be tuned by an external electric field while the other remains ferromagnetic. We simulate those results with ab initio calculations and explain them with a simple model based on a rigid shift of the bands associated with different spins. The model can be applied to similar van der Waal stacked insulating bilayer anti-ferromagnets.

We investigate the electronic density redistribution of rotated bilayer graphene under a perpendicular electric field, showing that the layers are actually coupled even for large angles. This layer-layer coupling is evidenced by the charge transfer on these structures as a function of the external voltage. We find an inhomogeneous excess charge distribution that is related to the moir\'e patterns for small angles, but that persists for larger angles where the carriers' velocity is equal to that of single layer graphene. Our results show that rotated bilayer systems are coupled for all rotation angles.

Twisted bilayer graphene is a chiral system which has been recently shown to present circular dichroism. In this work we show that the origin of this optical activity is the rotation of the Dirac fermions’ helicities in the top and bottom layer. Starting from the Kubo formula, we obtain a compact expression for the Hall conductivity that takes into account the dephasing of the electromagnetic field between the top and bottom layers and gathers all the symmetries of the system. Our results are based in both a continuum and a tight-binding model, and they can be generalized to any two-dimensional Dirac material with a chiral stacking between layers.