A Note in the Skyrme Model with Higher Derivative Terms

Another stabilizer term is used in the classical Hamiltonian of the Skyrme Model that permits in a much simple way the generalization of the higher-order terms in the pion derivative field. Improved numerical results are obtained.Comment: Latex. Figure not include; available upon request. 7 pages, report

Roughness correction to the Casimir force : Beyond the Proximity Force Approximation

We calculate the roughness correction to the Casimir effect in the parallel plates geometry for metallic plates described by the plasma model. The calculation is perturbative in the roughness amplitude with arbitrary values for the plasma wavelength, the plate separation and the roughness correlation length. The correction is found to be always larger than the result obtained in the Proximity Force Approximation.Comment: 7 pages, 3 figures, v2 with minor change

Kondo Quantum Criticality of Magnetic Adatoms in Graphene

We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in graphene, where the Kondo temperature scales as $T_{K}\propto|J-J_{c}|^{1/3}$ near the critical coupling $J_{c}$, and the local spin is effectively screened by a \emph{super-ohmic} bath. For this class, the RKKY interaction decays spatially with a fast power law $\sim1/R^{7}$. Away from half filling, we show that the exchange coupling in graphene can be controlled across the quantum critical region by gating. We propose that the vicinity of the Kondo quantum critical point can be directly accessed with scanning tunneling probes and gating.Comment: 4.1 pages, 3 figures. Added erratum correcting exponent nu=1/3. All the other results remain vali

Electron-Electron Interactions in the Vacuum Polarization of Graphene

We discuss the effect of electron-electron interactions on the static polarization properties of graphene beyond RPA. Divergent self-energy corrections are naturally absorbed into the renormalized coupling constant $\alpha$. We find that the lowest order vertex correction, which is the first non-trivial correlation contribution, is finite, and about 30% of the RPA result at strong coupling $\alpha \sim 1$. The vertex correction leads to further reduction of the effective charge. Finite contributions to dielectric screening are expected in all orders of perturbation theory.Comment: 5 pages, 2 figures; published versio

Electronic compressibility of a graphene bilayer

We calculate the electronic compressibility arising from electron-electron interactions for a graphene bilayer within the Hartree-Fock approximation. We show that, due to the chiral nature of the particles in this system, the compressibility is rather different from those of either the two-dimensional electron gas or ordinary semiconductors. We find that an inherent competition between the contributions coming from intra-band exchange interactions (dominant at low densities) and inter-band interactions (dominant at moderate densities) leads to a non-monotonic behavior of the compressibility as a function of carrier density.Comment: 4 pages, 4 figures. Final versio