We investigate the effect that the intrinsic spin-orbit and the interlayer and intralayer Rashba interactions have on the energy spectrum of either an unbiased or a biased graphene bilayer. We find that under certain conditions, a Dirac cone is formed out of a parabolic band and that it is possible to create a "Mexican hat"-like energy dispersion in an unbiased bilayer. In addition, in the presence of only an intralayer Rashba interaction, the K ͑KЈ͒ point splits into four distinct ones, contrarily to the case in single-layer graphene, where the splitting also takes place, but the low-energy dispersion at these points remains identical.

In this article we study the ferromagnetic behavior of ABC-stacked trilayer graphene. This is done using a nearest-neighbor tight-binding model, in the presence of long-range Coulomb interactions. For a given electronelectron interaction g and doping level n, we determine whether the total energy is minimized for a paramagnetic or ferromagnetic configuration of our variational parameters. The g versus n phase diagram is first calculated for the unscreened case. We then include the effects of screening using a simplified expression for the fermion bubble diagram. We show that ferromagnetism in ABC-stacked trilayer graphene is more robust than in monolayer, in bilayer, and in ABA-stacked trilayer graphene. Although the screening reduces the ferromagnetic regime in ABC-stacked trilayer graphene, the critical doping level remains one order of magnitude larger than in unscreened bilayer graphene.

We study the instability of the metallic state toward the formation of a different ground state in graphene doped near the van Hove singularity. The system is described by the Hubbard model and a field theoretical approach is used to calculate the charge and spin susceptibility. We find that for repulsive interactions, within the random phase approximation, there is a competition between ferromagnetism and the spin-density wave (SDW). It turns out that a SDW with a triangular geometry is more favorable when the Hubbard parameter is above the critical value U c (T ), which depends on the temperature T , even if there are small variations in the doping. Our results can be verified by angle-resolved photoemission spectroscopy or neutron scattering experiments in highly doped graphene.

In this paper, we study the static polarization in ABC-stacked multilayer graphene. Since the density of states diverges for these systems if the number of layers exceeds three, screening effects are expected to be important. In the random phase approximation, screening can be included through the polarization. We derive an analytical integral expression for the polarization in both the full-band model and an effective two-band model. Numerical evaluation of these integrals is very time consuming in the full-band model. Hence, for ABC-stacked trilayer graphene, we use the two-band model to calculate the low momentum part of the polarization. The results for the two-band model are universal, i.e., independent of doping. The high momentum part is linear and is determined by calculating two points, such that we can determine the slope. For ABC stacked trilayer graphene, the slope is given by three times the monolayer value. We compare our results to previous ones in the literature and discuss the similarities and discrepancies. Our results can be used to include screening in ABC-stacked multilayer systems in a way that all the characteristics of the polarization function are included. The numerical results for the polarization of trilayer graphene are used to sketch the screened potential.

We study the ground-state properties of an ABA-stacked trilayer graphene. The low-energy band structure can be described by a combination of both a linear and a quadratic particle-hole symmetric dispersion, reminiscent of monolayer and bilayer graphene, respectively. The multiband structure offers more channels for instability toward ferromagnetism when the Coulomb interaction is taken into account. Indeed, if one associates a subband-index 1/2 degree of freedom to the bands (parabolic and linear), it is possible to realize also a band-ferromagnetic state, where there is a shift in the energy bands since they fill up differently. By using a variational procedure, we compute the exchange energies for all possible variational ground states and identify the parameter space for the occurrence of spin-and band-ferromagnetic instabilities as a function of doping and interaction strength.