Melting temperature of screened Wigner crystal on helium films by molecular dynamics

Using molecular dynamics (MD) simulation, we have calculated the melting temperature of two-dimensional electron systems on $240$\AA-$500$\AA helium films supported by substrates of dielectric constants $\epsilon_{s}=2.2-11.9$ at areal densities $n$ varying from $3\times 10^{9}$ cm$^{-2}$ to $1.3\times 10^{10}$ cm$^{-2}$. Our results are in good agreement with the available theoretical and experimental results.Comment: 4 pages and 4 figure

Counterion-Mediated Weak and Strong Coupling Electrostatic Interaction between Like-Charged Cylindrical Dielectrics

We examine the effective counterion-mediated electrostatic interaction between two like-charged dielectric cylinders immersed in a continuous dielectric medium containing neutralizing mobile counterions. We focus on the effects of image charges induced as a result of the dielectric mismatch between the cylindrical cores and the surrounding dielectric medium and investigate the counterion-mediated electrostatic interaction between the cylinders in both limits of weak and strong electrostatic couplings (corresponding, e.g., to systems with monovalent and multivalent counterions, respectively). The results are compared with extensive Monte-Carlo simulations exhibiting good agreement with the limiting weak and strong coupling results in their respective regime of validity.Comment: 19 pages, 10 figure

Ion exchange phase transitions in "doped" water--filled channels

Ion transport through narrow water--filled channels is impeded by a high electrostatic barrier. The latter originates from the large ratio of the dielectric constants of the water and a surrounding media. We show that ``doping'', i.e. immobile charges attached to the walls of the channel, substantially reduces the barrier. This explains why most of the biological ion channels are ``doped''. We show that at rather generic conditions the channels may undergo ion exchange phase transitions (typically of the first order). Upon such a transition a finite latent concentration of ions may either enter or leave the channel, or be exchanged between the ions of different valences. We discuss possible implications of these transitions for the Ca-vs.-Na selectivity of biological Ca channels. We also show that transport of divalent Ca ions is assisted by their fractionalization into two separate excitations.Comment: 16 pages, 27 figure

Nanomechanical displacement detection using coherent transport in ordered and disordered graphene nanoribbon resonators

Graphene nanoribbons provide an opportunity to integrate phase-coherent transport phenomena with nanoelectromechanical systems (NEMS). Due to the strain induced by a deflection in a graphene nanoribbon resonator, coherent electron transport and mechanical deformations couple. As the electrons in graphene have a Fermi wavelength \lambda ~ a_0 = 1.4 {\AA}, this coupling can be used for sensitive displacement detection in both armchair and zigzag graphene nanoribbon NEMS. Here it is shown that for ordered as well as disordered ribbon systems of length L, a strain \epsilon ~ (w/L)^2 due to a deflection w leads to a relative change in conductance \delta G/G ~ (w^2/a_0L).Comment: 4 Pages, 4 figure

Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing treelike networks. The two interesting quantities are determined through the recurrence relations derived from the structure of the networks. Beginning from the rigorous relations one can obtain the complete eigenvalues and eigenvectors for the networks of arbitrary size. The analytical method opens the way to analytically compute the eigenvalues and eigenvectors of some other deterministic networks, making it possible to accurately calculate their spectral characteristics.Comment: Definitive version accepted for publication in Physical Reivew

Modelling background charge rearrangements near single-electron transistors as a Poisson process

Background charge rearrangements in metallic single-electron transistors are modelled in two-level tunnelling systems as a Poisson process with a scale parameter as only variable. The model explains the recent observation of asymmetric Coulomb blockade peak spacing distributions in metallic single-electron transistors. From the scale parameter we estimate the average size of the tunnelling systems, their density of states, and the height of their energy barrier. We conclude that the observed background charge rearrangements predominantly take place in the substrate of the single-electron transistor.Comment: 7 pages, 2 eps figures, used epl.cls macro include

Electrostatics of Edge States of Quantum Hall Systems with Constrictions: Metal--Insulator Transition Tuned by External Gates

The nature of a metal--insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions at integer bulk filling, as reported in recent experiments of Roddaro et al. [1], is addressed. We are particularly concerned here with the insulating behavior--the phenomena of backscattering enhancement induced at high gate voltages. Electrostatics calculations for QH systems with split gates performed here show that observations are not a consequence of interedge interactions near the point contact. We attribute the phenomena of backscattering enhancement to a splitting of the integer edge into conducting and insulating stripes, which enable the occurrence of the more relevant backscattering processes of fractionally charged quasiparticles at the point contact. For the values of the parameters used in the experiments we find that the conducting channels are widely separated by the insulating stripes and that their presence alters significantly the low-energy dynamics of the edges. Interchannel impurity scattering does not influence strongly the tunneling exponents as they are found to be irrelevant processes at low energies. Exponents of backscattering at the point contact are unaffected by interchannel Coulomb interactions since all channels have same chirality of propagation.Comment: 19 pages; To appear in Phys. Rev.

One dimensional Confinement of Electric Field and Humidity Dependent DNA Conductivity

The dependence of DNA assemblies conductance on relative humidity is investigated theoretically. Following earlier suggestions, we consider the ionic conductivity through the layers of water adsorbed by DNA molecules. The increase in humidity results in a growing water layer. The binding energy of ions depends on the thickness of the water layer due to change in water polarization. This dependence is very strong at smaller thicknesses of water layers due to the low-dimensional confinement of an electric field in water. We show that the associated change in ion concentration can explain the six orders of magnitude increase in conductivity, with relative humidity growing from 0.05 to 0.95Comment: 16 pages, 5 figures, published in Journal of Chemical Physic

Control of the Casimir force by the modification of dielectric properties with light

The experimental demonstration of the modification of the Casimir force between a gold coated sphere and a single-crystal Si membrane by light pulses is performed. The specially designed and fabricated Si membrane was irradiated with 514 nm laser pulses of 5 ms width in high vacuum leading to a change of the charge-carrier density. The difference in the Casimir force in the presence and in the absence of laser radiation was measured by means of an atomic force microscope as a function of separation at different powers of the absorbed light. The total experimental error of the measured force differences at a separation of 100 nm varies from 10 to 20% in different measurements. The experimental results are compared with theoretical computations using the Lifshitz theory at both zero and laboratory temperatures. The total theoretical error determined mostly by the uncertainty in the concentration of charge carriers when the light is incident is found to be about 14% at separations less than 140 nm. The experimental data are consistent with the Lifshitz theory at laboratory temperature, if the static dielectric permittivity of high-resistivity Si in the absence of light is assumed to be finite. If the dc conductivity of high-resistivity Si in the absence of light is included into the model of dielectric response, the Lifshitz theory at nonzero temperature is shown to be experimentally inconsistent at 95% confidence. The demonstrated phenomenon of the modification of the Casimir force through a change of the charge-carrier density is topical for applications of the Lifshitz theory to real materials in fields ranging from nanotechnology and condensed matter physics to the theory of fundamental interactions.Comment: 30 pages, 10 figures, 2 table

Degree and component size distributions in generalized uniform recursive tree

We propose a generalized model for uniform recursive tree (URT) by introducing an imperfect growth process, which may generate disconnected components (clusters). The model undergoes an interesting phase transition from a singly connected network to a graph consisting of fully isolated nodes. We investigate the distributions of degree and component sizes by both theoretical predictions and numerical simulations. For the nontrivial cases, we show that the network has an exponential degree distribution while its component size distribution follows a power law, both of which are related to the imperfect growth process. We also predict the growth dynamics of the individual components. All analytical solutions are successfully contrasted with computer simulations.Comment: 4 pages, 3 figure