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

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.

Interaction of vortices in thin superconducting films and Berezinskii-Kosterlitz-Thouless transition

The precondition for the BKT transition in thin superconducting films, the logarithmic intervortex interaction, is satisfied at distances short relative to $\Lambda=2\lambda^2/d$, $\lambda$ is the London penetration depth of the bulk material and $d$ is the film thickness. For this reason, the search for the transition has been conducted in samples of the size $L<\Lambda$. It is argued below that film edges turn the interaction into near exponential (short-range) thus making the BKT transition impossible. If however the substrate is superconducting and separated from the film by an insulated layer, the logarithmic intervortex interaction is recovered and the BKT transition should be observable.Comment: 4 pages, no figure

On the uniqueness of the surface sources of evoked potentials

The uniqueness of a surface density of sources localized inside a spatial region $R$ and producing a given electric potential distribution in its boundary $B_0$ is revisited. The situation in which $R$ is filled with various metallic subregions, each one having a definite constant value for the electric conductivity is considered. It is argued that the knowledge of the potential in all $B_0$ fully determines the surface density of sources over a wide class of surfaces supporting them. The class can be defined as a union of an arbitrary but finite number of open or closed surfaces. The only restriction upon them is that no one of the closed surfaces contains inside it another (nesting) of the closed or open surfaces.Comment: 16 pages, 5 figure

Modifying the Casimir force between indium tin oxide film and Au sphere

We present complete results of the experiment on measuring the Casimir force between an Au-coated sphere and an untreated or, alternatively, UV-treated indium tin oxide film deposited on a quartz substrate. Measurements were performed using an atomic force microscope in a high vacuum chamber. The measurement system was calibrated electrostatically. Special analysis of the systematic deviations is performed, and respective corrections in the calibration parameters are introduced. The corrected parameters are free from anomalies discussed in the literature. The experimental data for the Casimir force from two measurement sets for both untreated and UV-treated samples are presented. The experimental errors are determined at a 95% confidence level. It is demonstrated that the UV treatment of an I TO plate results in a significant decrease in the magnitude of the Casimir force (from 21% to 35% depending on separation). However, ellipsometry measurements of the imaginary parts of dielectric permittivities of the untreated and UV-treated samples did not reveal any significant differences. The experimental data are compared with computations in the framework of the Lifshitz theory. It is found that the data for the untreated sample are in a very good agreement with theoretical results taking into account the free charge carriers in an ITO film. For the UV-treated sample the data exclude the theoretical results obtained with account of free charge carriers. These data are in a very good agreement with computations disregarding the contribution of free carriers. According to the explanation provided, this is caused by the phase transition of the ITO film from metallic to dielectric state caused by the UV treatment. Possible applications of the discovered phenomenon in nanotechnology are discussed.Comment: 30 pages, 19 figures, 1 tabl

Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using atomic force microscope in a frequency shift technique

We present measurement results for the gradient of the Casimir force between an Au-coated sphere and an Au-coated plate obtained by means of an atomic force microscope operated in a frequency shift technique. This experiment was performed at a pressure of 3x10^{-8} Torr with hollow glass sphere of 41.3 mcm radius. Special attention is paid to electrostatic calibrations including the problem of electrostatic patches. All calibration parameters are shown to be separation-independent after the corrections for mechanical drift are included. The gradient of the Casimir force was measured in two ways with applied compensating voltage to the plate and with different applied voltages and subsequent subtraction of electric forces. The obtained mean gradients are shown to be in mutual agreement and in agreement with previous experiments performed using a micromachined oscillator. The obtained data are compared with theoretical predictions of the Lifshitz theory including corrections beyond the proximity force approximation. An independent comparison with no fitting parameters demonstrated that the Drude model approach is excluded by the data at a 67% confidence level over the separation region from 235 to 420 nm. The theoretical approach using the generalized plasma-like model is shown to be consistent with the data over the entire measurement range. Corrections due to the nonlinearity of oscillator are calculated and the application region of the linear regime is determined. A conclusion is made that the results of several performed experiments call for a thorough analysis of the basics of the theory of dispersion forces.Comment: 35 pages, 14 figures, 1 table; to appear in Phys. Rev.

Equation of the field lines of an axisymmetric multipole with a source surface

Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map the surface magnetic fields of forming solar-like stars, which are still contracting under gravity and are surrounded by a disk of gas and dust. Their large scale magnetic fields are almost dipolar on some stars, and there is evidence for many higher order multipole field components on other stars. The availability of new data has renewed interest in incorporating multipolar magnetic fields into models of stellar magnetospheres. I describe the basic properties of axial multipoles of arbitrary degree ℓ and derive the equation of the field lines in spherical coordinates. The spherical magnetic field components that describe the global stellar field topology are obtained analytically assuming that currents can be neglected in the region exterior to the star, and interior to some fixed spherical equipotential surface. The field components follow from the solution of Laplace’s equation for the magnetostatic potential

Steplike electric conduction in a classical two-dimensional electron system through a narrow constriction in a microchannel

Using molecular dynamics simulation, we investigate transport properties of a classical two-dimensional electron system confined in a microchannel with a narrow constriction. As a function of the confinement strength of the constriction, the calculated conductance in the simulations exhibits steplike increases as reported in a recent experiment [D. G. Rees et al., Phys. Rev. Lett. 106, 026803 (2011)]. It is confirmed that the number of the steps corresponds to the number of stream lines of electrons through the constriction. We verify that density fluctuation plays a major role in smoothing the steps in the conductance.Comment: 11 pages, 9 figure

Addition-Deletion Networks

We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly selected existing node. With rate 1, a randomly selected node is deleted, and its parent node inherits the links of its immediate descendants. We show that the in-component size distribution decays algebraically, c_k ~ k^{-beta}, as k-->infty. The exponent beta=2+1/(r-1) varies continuously with the addition rate r. Structural properties of the network including the height distribution, the diameter of the network, the average distance between two nodes, and the fraction of dangling nodes are also obtained analytically. Interestingly, the deletion process leads to a giant hub, a single node with a macroscopic degree whereas all other nodes have a microscopic degree.Comment: 8 pages, 5 figure

Diffraction of light by a planar aperture in a metallic screen

We present a complete derivation of the formula of Smythe [Phys.Rev.72, 1066 (1947)] giving the electromagnetic field diffracted by an aperture created in a perfectly conducting plane surface. The reasoning, valid for any excitating field and any hole shape, makes use only of the free scalar Green function for the Helmoltz equation without any reference to a Green dyadic formalism. We compare our proof with the one previously given by Jackson and connect our reasoning to the general Huygens Fresnel theorem.Comment: J. Math. Phys. 47, 072901 (2006