Ravi Mehrotra

Analysis of the Sommer technique for measurement of the mobility for charges in two dimensions

The technique for measuring the low-frequency ac mobility of free surface charges first employed by Sommer is analyzed for arbitrary values of driving frequency, charge mobility, and effective mass. Analytical expressions for the cell admittance are given for both rectangular and circular geometries in the absence of edge corrections.

Density and capacitance profiles and edge effects in a two-dimensional charge layer on a dielectric surface

The density and capacitance profiles and edge effects in a two-dimensional (2D) layer of electrons held on a liquid helium surface between two horizontal plates of a parallel-plate capacitor are studied by solving Laplaces equation on a computer. An effective length for experimental cells is defined to take into account nonuniform charge density and capacitance near the edges of the cells. The profiles and edge effects are studied as a function of charge density on the helium surface, helium depth inside the cell, repelling voltages on guard electrodes around the capacitor plates, and the frequency of excitation. The results should be useful in designing cells for experiments and better analyzing the results of measurements.

Molecular dynamics simulations on a classical quasi-one-dimensional electron system

Abstract A classical system of electrons confined in a strip geometry has been studied by the method of Molecular Dynamics as a function of the plasma parameter Γ. The boundary conditions for the simulations are periodic along the length of the strip and open across its width. Systems of various sizes with N x ≤50 electrons along the length and N y =8 electrons across the width have been investigated. The value of Γ at melting Γ c plotted versus N x shows steps in the range Γ c ≈275–550. For Γ c , the systems melts to form a novel anisotropic stat with N y parallel one-dimensional electron systems along the length of the strip.

Viscoelastic effects in a two-dimensional classical electron liquid

The shear viscosity of a classical two-dimensional (2D) electron liquid is estimated by adapting the theory of Kirkwood, Buff, and Green for three dimensions to two dimensions. It is found to be large enough so that shear modes, if not overdamped by other scattering mechanisms, should be able to propagate through the electron liquid above a minimum temperature-dependent frequency, which is a small fraction of the highest frequency in the corresponding 2D electron solid.

The dynamical response of a three-junction network II: vortices

Abstract The phase diagram of a triangular network of overdamped Josephson Junctions driven by independent current drives is studied in terms of vortices. There are no vortices in the fixed-point region, while in the p q Arnold tongue, vortices appear in sequences which repeat themselves every q vortices. Precisely q − p vortices in each sequence are injected by the non-uniform drive. We explicitly identify the vortex sequence at infinity and find that for large input currents, all reals between 1 and 1 2 can be given a unique binary representation in terms of vortices.

Fast algorithms for Josephson-junction arrays: Busbars and defects.

We critically review the fast algorithms for the numerical study of two–dimensional Josephson junction arrays and develop the analogy of such systems with electrostatics. We extend these procedures to arrays with bus–bars and defects in the form of missing bonds. The role of boundaries and of the guage choice in determing the Green’s function of the system is clarified. The extension of the Green’s function approach to other situations is also discussed. The dynamical properties of Josephson junction arrays (JJAs) are currently the foci of several experimental and theoretical investigations [1]. These arrays can now be routinely fabricated in several sizes and geometries, and the characteristics of their junctions can be varied at will over a wide range of values [2]. A large body of high–precision experimental data has consequently become available for JJAs in the presence of external magnetic fields [3–5]. On the theoretical front, several insights into the behaviour of JJAs have come from numerical studies of the underlying equations of motion as given by the resistively- and capacitively-shunted junction (RCSJ) model using input current drives and defects, both controlled [6] and random [7]. With the size of experimental arrays increasing continuously, and with the number of interesting effects best seen only in large arrays going up in equal measure, it has become imperative to find ever more efficient algorithms for implementing the corresponding simulations, inclusive of all the experimental conditions. An example of the latter for current–driven arrays is the presence of bus-bars, through which the external current can be conveniently injected or withdrawn. To understand the problem which these algorithms must address, we recall that in the RCSJ model, the total current, iij, (inclusive of external drives where applicable) flowing through the junction between sites i and j, is viewed as consisting of three ‘channels’ in parallel: superconductive, resistive ( or ohmic) and capacitive. The currents in each of these channels can be expressed in terms of the phase difference, θij = θi − θj, across the junction. This leads to the following equation for the evolution of the latter in time: C¯

Chaos and dynamics of vortices in Josephson junction arrays

Abstract The approach to spatiotemporal chaos in two-dimensional (2D) Josephson junction arrays (JJAs) subjected to DC current drives is reviewed. The role of vortices in describing the various transitions and types of dynamical behaviour that occur is explored. Some analogies with hydrodynamics are found.

VORTEX PINNING AND CRITICAL CURRENTS IN JOSEPHSON JUNCTION ARRAYS WITH DEFECTS

We develop an algorithm based on the Fast Cosine Transform to study two-dimensional arrays of Josephson junctions containing defects. We apply it to arrays as large as 128 × 256 and study vortex pinning, the transition from the superconducting to the resistive state, and various finite size effects. We find that the pinning potential for vortices is highly anisotropic in rectangular arrays due to boundaries and finite size effects. As a result we observe pinned vortices in arrays much smaller than expected so far. The energy of an array changes discontinuously at transitions from one vortex sector to another in the steady-state regime.

High resolutionV-I characteristics measurements on highT c superconductors

V-I characteristics of sintered superconducting pellets of YBa2Cu3O7−δ was measured with a resolution one order of magnitude better than the usual dc techniques employing nanovoltmeters. For this purpose software-based lock-in-amplifier technique was developed and used. A square-wave excitation current was used. The voltage signal was digitized into a time series and Fourier-analysed on a computer in this technique. Our results show a very small frequency-dependent resistance in some samples which are nominally superconducting. These results help in checking the material quality and defining the critical current densities better.

Indirect evidence for the existence of viscoelastic shear modes in a two-dimensional classical electron liquid

It has recently been predicted that viscoelastic shear modes should propagate in a two-dimensional (2D) classical electron liquid above a minimum temperature dependent frequency. A 2D electron layer held above a liquid helium substrate is considered in this paper. The contribution of scattering between viscoelastic shear modes of the electron fluid and ripplons on the liquid helium surface to the mobility of electrons is calculated. This contribution explains the differences observed between the existing experimental data and single electron-ripplon scattering calculations quite well. This may be taken as indirect evidence for the existence of viscoelastic shear modes in a 2D electron liquid.