Abstract: Using the tight-binding formalism we show that in the recently experimentally realized AA-stacked graphite in essence two types of massless relativistic Dirac particles are present with a different effective speed of light. We also investigate how the electronic structure evolves from a single graphene sheet into AA-stacked graphite. It is shown that in contrast to AB-stacked graphene layers, the spectrum of AA-stacked graphene layers can be considered as a superposition of single-layer spectra and only particles with a linear spectrum at the Fermi energy around the K point are present. From the evolution of the band overlap we show that 6 multilayers of AA-stacked graphene already behave as AA-stacked graphite. The evolution of the effective speeds of light of the Dirac particles to their bulk values shows exactly the same behavior. The tight-binding parameters we use to describe AA-stacked graphite and multilayers of graphene are obtained by ab initio calculations.

Abstract: Nanoindentation of bilayer graphene is studied using molecular-dynamics simulations. We compared our simulation results with those from elasticity theory as based on the nonlinear Föppl-Hencky equations with rigid boundary condition. The force-deflection values of bilayer graphene are compared to those of monolayer graphene. Youngs modulus of bilayer graphene is estimated to be 0.8 TPa which is close to the value for graphite. Moreover, an almost flat bilayer membrane at low temperature under central load has a 14% smaller Youngs modulus as compared to the one at room temperature.

Abstract: The electric-field response of a one-dimensional ring of interacting fermions, where the interactions are described by the extended Hubbard model, is investigated. By using an accurate real-time propagation scheme based on the Chebyshev expansion of the evolution operator, we uncover various nonlinear regimes for a range of interaction parameters that allows modeling of metallic and insulating (either charge density wave or spin density wave insulators) rings. The metallic regime appears at the phase boundary between the two insulating phases and provides the opportunity to describe either weakly or strongly correlated metals. We find that the fidelity susceptibility of the ground state as a function of magnetic flux piercing the ring provides a very good measure of the short-time response. Even completely different interacting regimes behave in a similar manner at short time scales as long as the ground-state fidelity susceptibility is the same. Depending on the strength of the electric field we find various types of responses: persistent currents in the insulating phase, a dissipative regime, or damped Bloch-like oscillations with varying frequencies or even irregular in nature. Furthermore, we also consider the dimerization of the ring and describe the response of a correlated band insulator. In this case the distribution of the energy levels is more clustered and the Bloch-like oscillations become even more irregular.