We present an analytical theory for the gate electrostatics and the classical and quantum capacitance of the graphene nanoribbons (GNRs) and compare it with the exact self-consistent numerical calculations based on the tight-binding p-orbital Hamiltonian within the Hartree approximation. We demonstrate that the analytical theory is in a good qualitative (and in some aspects quantitative) agreement with the exact calculations. There are however some important discrepancies. In order to understand the origin of these discrepancies we investigate the self-consistent electronic structure and charge density distribution in the nanoribbons and relate the above discrepancy to the inability of the simple electrostatic model to capture the classical gate electrostatics of the GNRs. In turn, the failure of the classical electrostatics is traced to the quantum mechanical effects leading to the significant modification of the self-consistent charge distribution in comparison to the non-interacting electron description. The role of electron-electron interaction in the electronic structure and the capacitance of the GNRs is discussed. Our exact numerical calculations show that the density distribution and the potential profile in the GNRs are qualitatively different from those in conventional split-gate quantum wires; at the same time, the electron distribution and the potential profile in the GNRs show qualitatively similar features to those in the cleaved-edge overgrown quantum wires. Finally, we discuss an experimental extraction of the quantum capacitance from experimental data.Comment: 9 pages, 5 figures, submitted to PR

By combining Brillouin Light Scattering and micromagnetic simulations we studied the spin-wave dynamics of a Co/Pd thin film multilayer, features a stripe domain structure at remanence. The periodic up and down domains are separated by cork-screw type domain walls. The existence of these domains causes a scattering of the otherwise bulk and surface spin-wave modes, which form mode families, similar to a one dimensional magnonic crystal. The dispersion relation and mode profiles of spin waves are measured for transferred wave vector parallel and perpendicular to the domain axis.The possibility to use spin-waves (SW) to excite, transmit, store, and retrieve electric signals as well as to perform logical operations has fueled a new spectrum of research in the wavebased signal processing technology [1-4]. Usually, magnonic crystals (MC), i.e. arrays of macroscopic magnetic stripes [5], dots [6], antidots [7], etched grooves or pits[1], periodic variations of the internal magnetic field [9] and saturation magnetization by ion implantation [10], are employed to control the flow of SWs. Magnetostatic surface SWs or the Damon-Eshbach (DE) SW modes, which propagate perpendicular to the in-plane (IP) magnetization direction, are promising in this context because of their large group velocities (vg) and low attenuation.Consequently, significant progress has been made towards the practical realization of magnonic devices in terms of the on-chip generation, directional channeling, detection and manipulation of SWs. However, to realize the experimental geometry, a large magnetic field has to be applied to enforce the magnetization perpendicular to the SW propagation direction. This is a major obstacle to the implementation of a MC into a practical device. A way out is to use the Oersted field generated from an underlying current-carrying stripe [11][12], which is still plagued by the problem of generation of waste heat which increases with increasing data processing speed. Moreover, the fabrication of periodic nanostructures involves high-precision electron-beam lithography which is very complex and expensive. An alternative approach to overcome these fundamental drawbacks is to take recourse to the spin dynamics in the remanent state, which is more suitable for nanoscale device applications, as it does not require any stand-by power once initialized.In the literature, only few reports exist on the magnetization dynamics for systems with an inhomogeneous magnetization distribution containing domains and domain walls. Most commonly studied is a periodic or non-periodic distribution of magnetic units of up and down domains (parallel, labyrinthine, bubble-like domains) [13][14][15][16][17][18][19], separated by negligibly thin, onedimensional domain walls. Such domains appear in magnetic thin films with a perpendicular anisotropy smaller than the demagnetizing energy if the film thickness is higher than a critical value tc, which is, in turn, dependent on the perpendicular anisotropy constant, saturation magnetization and the exc...

We present a comparative study of the density dependence of the conductivity of graphene sheets calculated in the tight-binding ͑TB͒ Landauer approach and on the basis of the Boltzmann theory. The TB calculations are found to give the same density dependence of the conductivity, TB ϳ n, for short-and long-range Gaussian scatterers. In the case of short-range scattering the TB calculations are in agreement with the predictions of the Boltzmann theory going beyond the Born approximation but in qualitative and quantitative disagreement with the standard Boltzmann approach within the Born approximation, predicting Boltz = const. Even for the longrange Gaussian potential in a parameter range corresponding to realistic systems the standard Boltzmann predictions are in quantitative and qualitative disagreement with the TB results. This questions the applicability of the standard Boltzmann approach within the Born approximation, commonly used for the interpretation of the results of experimental studies of the transport in graphene.

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