Ionic screening of charged impurities in electrolytically gated graphene: A partially linearized Poisson-Boltzmann model.

We present a model describing the electrostatic interactions across a structure that consists of a single layer of graphene with large area, lying above an oxide substrate of finite thickness, with its surface exposed to a thick layer of liquid electrolyte containing salt ions. Our goal is to analyze the co-operative screening of the potential fluctuation in a doped graphene due to randomness in the positions of fixed charged impurities in the oxide by the charge carriers in graphene and by the mobile ions in the diffuse layer of the electrolyte. In order to account for a possibly large potential drop in the diffuse later that may arise in an electrolytically gated graphene, we use a partially linearized Poisson-Boltzmann (PB) model of the electrolyte, in which we solve a fully nonlinear PB equation for the surface average of the potential in one dimension, whereas the lateral fluctuations of the potential in graphene are tackled by linearizing the PB equation about the average potential. In this way, we are able to describe the regime of equilibrium doping of graphene to large densities for arbitrary values of the ion concentration without restrictions to the potential drop in the electrolyte. We evaluate the electrostatic Green's function for the partially linearized PB model, which is used to express the screening contributions of the graphene layer and the nearby electrolyte by means of an effective dielectric function. We find that, while the screened potential of a single charged impurity at large in-graphene distances exhibits a strong dependence on the ion concentration in the electrolyte and on the doping density in graphene, in the case of a spatially correlated two-dimensional ensemble of impurities, this dependence is largely suppressed in the autocovariance of the fluctuating potential.

Modeling Electrolytically Top-Gated Graphene.

We investigate doping of a single-layer graphene in the presence of electrolytic top gating. The interfacial phenomenon is modeled using a modified Poisson-Boltzmann equation for an aqueous solution of simple salt. We demonstrate both the sensitivity of graphene's doping levels to the salt concentration and the importance of quantum capacitance that arises due to the smallness of the Debye screening length in the electrolyte.

Friction force on slow charges moving over supported graphene.

We provide a theoretical model that describes the dielectric coupling of a two-dimensional (2D) layer of graphene, represented by a polarization function in the random phase approximation, and a semi-infinite three-dimensional (3D) substrate, represented by a surface response function in a non-local formulation. We concentrate on the role of the dynamic response of the substrate for low-frequency excitations of the combined graphene-substrate system, which give rise to the stopping force on slowly moving charges above doped graphene. A comparison of the dielectric loss function with experimental high-resolution electron energy loss spectroscopy (HREELS) data for graphene on a SiC substrate is used to estimate the effects of damping rate and the local field correction in graphene, as well as to reveal the importance of phonon excitations in an insulating substrate. While the local field correction and linearly dispersing damping rate did not yield any important effects compared to the constant damping rate in graphene, a strong signature of the hybridization between graphene's pi plasmon and the substrate's phonon is found in both the HREELS spectra and the stopping force. A friction coefficient that is calculated for slow charges moving above graphene on a metallic substrate shows an interplay between the low-energy single-particle excitations in both systems.

Wave spectra of two-dimensional dusty plasma solids and liquids.

Brownian dynamics simulations were carried out to study wave spectra of two-dimensional dusty plasma liquids and solids for a wide range of wavelengths. The existence of a longitudinal dust-thermal mode was confirmed in simulations, and a cutoff wave number in the transverse mode was measured. Dispersion relations, resulting from simulations, were compared with those from analytical theories, such as the random-phase approximation (RPA), the quasilocalized charged approximation (QLCA), and the harmonic approximation (HA). An overall good agreement between the QLCA and simulations was found for wide ranges of states and wavelengths after taking into account the direct thermal effect in the QLCA, while for the RPA and HA, good agreement with simulations was found in the high and low-temperature limits, respectively.

Image force on a charged projectile moving over a two-dimensional strongly coupled Yukawa system.

We use both analytical theory and numerical simulations to study the image force on a charged particle moving parallel to a two-dimensional strongly coupled Yukawa system. Special attention is paid to the effects of strong correlation and nonlinear response in the Yukawa system on the dependences of the image force on the particle velocity and its distance from the Yukawa system. Those effects are elucidated by comparing the results obtained from a Brownian dynamics simulation with those from linear-dielectric-response theories based on both the quasilocalized charge approximation and the standard Vlasov random phase approximation.

Channelling of dipolar molecules through carbon nanotubes.

We study the dynamic polarization of carbon nanotubes caused by the propagation of fast electric dipoles under channelling conditions. We specifically analyse the position and orientation dependences of the dipole self-energy, stopping force, and the torque about the dipole centre. It is found that a dipole is strongly attracted to the nanotube wall and shows a tendency to orient itself perpendicular to the direction of motion. The stopping force shows more complex behaviour, but is generally found to be larger close to the nanotube wall and when oriented in the perpendicular direction at higher speeds.

Energy loss of a charged particle moving over a 2D strongly coupled dusty plasma.

We use molecular dynamics (MD) simulation to evaluate the energy loss of a charged projectile moving parallel to a two-dimensional strongly coupled dusty plasma and compare the results with those obtained from the quasilocalized charge approximation (QLCA) and the Vlasov-random phase approximation. Good agreement is found between the QLCA and MD results when the projectile-dust coupling is weak. In the opposite regime, nonlinear effects in the dust-layer response render the QLCA model increasingly inadequate for calculating the energy losses at low projectile speeds.

Excitation of Mach cones and energy dissipation by charged particles moving over two-dimensional strongly coupled dusty plasmas.

We present a theoretical model for studying the interactions of charged particles with two-dimensional strongly coupled dusty plasmas, based on the quasilocalized charge approximation in which the static pair distribution function of a dust layer is determined from a molecular dynamics simulation. General expressions are derived for the perturbed dust-layer density, the induced potential in plasma, and the energy loss of a charged particle moving parallel to the dust layer. Numerical results show that the structure of Mach cones, excited in the dust layer by the charged particle, strongly depends on the plasma parameters such as the coupling parameter, the screening parameter, and the discharge pressure, as well as on the particle speed. In addition, it is found that the energy dissipation suffered by slow charged particles can be significantly enhanced in strongly coupled dusty plasmas when compared to the dissipation in weakly coupled plasmas.

Theoretical study of laser-excited Mach cones in dusty plasmas.

A two-dimensional hydrodynamic model for a monolayer of dust particles is used to study the Mach cones excited by a moving laser beam through dusty plasmas. Numerical results for the density perturbation and the velocity distribution of dust particles exhibit both compressional and shear-wave Mach cones. It is found that the compressional Mach cones exist in cases of both supersonic and subsonic excitations, and that they consist of multiple lateral or transverse wakes. On the other hand, realization of single shear-wave Mach cones depends closely on the excitation technique, the laser scanning speed, and the discharge pressures. It is found that, when the scanning direction of the laser beam is perpendicular to the laser force, a transition from multiple compressional Mach cones to a single shear Mach cone can be achieved either by lowering the scanning speed or by increasing the discharge pressures.

Coulomb explosions and energy loss of molecular ions in plasmas.

Interactions of swift molecular ions with high-density plasma targets are studied by means of the linearized Vlasov-Poisson theory, allowing the dynamically screened interaction potential among the constituent ions to be expressed in terms of the classical plasma dielectric function. Coulomb explosions and the energy losses of a molecular ion are simulated by solving the equations of motion for the constituent ions. It is found that, due to the wakelike asymmetry of the interaction potential, the molecular axis tends to align itself along the beam direction. In addition, a strong enhancement of the energy loss of the molecular ion has been found in the initial stages of Coulomb explosions due to proximity of the constituent ions, but this effect diminishes at latter stages when the ions are sufficiently far apart.

Induced potential of a dust particle in a collisional radio-frequency sheath.

A hydrodynamic model is established to study the interactions of a dust particle with a radio-frequency (rf) sheath, taking into account the influence of the spatial inhomogeneity of the (rf) sheath, as well as the influence of the ion-neutral collisions. Numerical results are obtained for the charge on the dust particle and for the spatial distribution of the induced potential around this particle, based on a self-consistent modeling of the sheath parameters such as the sheath electric field, the ion velocity, and the ion and electron densities. The induced potential exhibits the familiar oscillatory structure of a wake potential, which is, however, strongly damped due to the collisional effects. The spatial inhomogeneity of the rf sheath gives rise to a further damping of the induced potential, as well as to a reduction of the oscillations at large distances from the dust particle.

Interaction potential among dust grains in a plasma with ion flow.

Linear-response dielectric theory is used to study the interaction potential between dust grains in a flowing plasma, taking into account the finite sizes and the asymmetric charge distributions of the grains. This potential can be divided into two parts: a screened Coulomb potential and a wake potential. The former is a short-ranged repulsive potential, while the later is a long-ranged oscillatory potential which acts only on trailing grains. Both the amplitude and wavelength of the wake potential depend on the Mach number. The grain size and the asymmetric charge distribution may affect the interaction potential in a significant way when the distances between grains are comparable with the grain size, or when the grain size is comparable with the plasma Debye length.