Shot noise variation within ensembles of gold atomic break junctions at room temperature.

Atomic-scale junctions are a powerful tool to study quantum transport, and are frequently examined through the mechanically controllable break junction technique. The junction-to-junction variation of atomic configurations often leads to a statistical approach, with ensemble-averaged properties providing access to the relevant physics. However, the full ensemble contains considerable additional information. We report a new analysis of shot noise over entire ensembles of junction configurations using scanning tunneling microscope-style gold break junctions at room temperature in ambient conditions, and compare these data with simulations based on molecular dynamics, a sophisticated tight-binding model, and nonequilibrium Green's functions. The experimental data show a suppression in the variation of the noise near conductances dominated by fully transmitting channels, and a surprising participation of multiple channels in the nominal tunneling regime. Comparison with the simulations, which agree well with published work at low temperatures and ultrahigh vacuum conditions, suggests that these effects likely result from surface contamination and disorder in the electrodes. We propose additional experiments that can distinguish the relative contributions of these factors.

A current-driven single-atom memory.

The possibility of fabricating electronic devices with functional building blocks of atomic size is a major driving force of nanotechnology. The key elements in electronic circuits are switches, usually realized by transistors, which can be configured to perform memory operations. Electronic switches have been miniaturized all the way down to the atomic scale. However, at such scales, three-terminal devices are technically challenging to implement. Here we show that a metallic atomic-scale contact can be operated as a reliable and fatigue-resistant two-terminal switch. We apply a careful electromigration protocol to toggle the conductance of an aluminium atomic contact between two well-defined values in the range of a few conductance quanta. Using the nonlinearities of the current-voltage characteristics caused by superconductivity in combination with molecular dynamics and quantum transport calculations, we provide evidence that the switching process is caused by the reversible rearrangement of single atoms. Owing to its hysteretic behaviour with two distinct states, this two-terminal switch can be used as a non-volatile information storage element.

Non-monotonic crossover from single-file to regular diffusion in micro-channels.

The diffusion behavior of interacting particles determines the behavior of a large number of systems ranging from pedestrians crossing a road to ions passing through channels in living cells. Here we present a system in which the nature of the diffusion process varies with changes in the external conditions. We find this special behavior in a colloidal model system, consisting of micron sized particles which are confined to narrow channels and interact via induced magnetic dipoles. When the density of these particles is changed, diffusion alternates between normal Fickian behavior and single-file diffusion. This anomalous behavior is induced by the order of the particles in the restricted geometry and does not depend on the exact nature of the inter-particle interactions.

Effects of confinement and external fields on structure and transport in colloidal dispersions in reduced dimensionality.

In this work, we focus on low-dimensional colloidal model systems, via simulation studies and also some complementary experiments, in order to elucidate the interplay between phase behavior, geometric structures and transport properties. In particular, we try to investigate the (nonlinear!) response of these very soft colloidal systems to various perturbations: uniform and uniaxial pressure, laser fields, shear due to moving boundaries and randomly quenched disorder. We study ordering phenomena on surfaces or in monolayers by Monte Carlo computer simulations of binary hard-disk mixtures, the influence of a substrate being modeled by an external potential. Weak external fields allow a controlled tuning of the miscibility of the mixture. We discuss the laser induced de-mixing for the three different possible couplings to the external potential. The structural behavior of hard spheres interacting with repulsive screened Coulomb or dipolar interaction in 2D and 3D narrow constrictions is investigated using Brownian dynamics simulations. Due to misfits between multiples of the lattice parameter and the channel widths, a variety of ordered and disordered lattice structures have been observed. The resulting local lattice structures and defect probabilities are studied for various cross sections. The influence of a self-organized order within the system is reflected in the velocity of the particles and their diffusive behavior. Additionally, in an experimental system of dipolar colloidal particles confined by gravity on a solid substrate we investigate the effect of pinning on the dynamics of a two-dimensional colloidal liquid. This work contains sections reviewing previous work by the authors as well as new, unpublished results. Among the latter are detailed studies of the phase boundaries of the de-mixing regime in binary systems in external light fields, configurations for shear induced effects at structured walls, studies on the effect of confinement on the structures and defect densities in three-dimensional systems, the effect of confinement and barriers on two-dimensional flow and diffusion, and the effect of pinning sites on the diffusion.

Coarse-graining microscopic strains in a harmonic, two-dimensional solid: elasticity, nonlocal susceptibilities, and nonaffine noise.

In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli in these systems using a coarse-graining procedure. We study this process in detail for a simple triangular, harmonic lattice in two dimensions. Coarse-graining local strains obtained from particle configurations in a Monte Carlo simulation generates nontrivial, nonlocal strain correlations (susceptibilities). These may be understood within a generalized, Landau-type elastic Hamiltonian containing up to quartic terms in strain gradients [K. Franzrahe, Phys. Rev. E 78, 026106 (2008)10.1103/PhysRevE.78.026106]. In order to demonstrate the versatility of the analysis of these correlations and to make our calculations directly relevant for experiments on colloidal solids, we systematically study various parameters such as the choice of statistical ensemble, presence of external pressure and boundary conditions. Crucially, we show that special care needs to be taken for an accurate application of our results to actual experiments, where the analyzed area is embedded within a larger system, to which it is mechanically coupled. Apart from the smooth, affine strain fields, the coarse-graining procedure also gives rise to a noise field (χ) made up of nonaffine displacements. Several properties of χ may be rationalized for the harmonic solid using a simple "cell model" calculation. Furthermore the scaling behavior of the probability distribution of the noise field (χ) is studied. We find that for any inverse temperature ß, spring constant f, density ρ and coarse-graining length Λ the probability distribution can be obtained from a master curve of the scaling variable X=χßf/ρΛ(2).

Density reduction and diffusion in driven two-dimensional colloidal systems through microchannels.

The behavior of particles driven through a narrow constriction is investigated in experiment and simulation. The system of particles adapts to the confining potentials and the interaction energies by a self-consistent arrangement of the particles. It results in the formation of layers throughout the channel and of a density gradient along the channel. The particles accommodate to the density gradient by reducing the number of layers one by one when it is energetically favorable. The position of the layer reduction zone fluctuates with time while the particles continuously pass this zone. The flow behavior of the particles is studied in detail. The velocities of the particles and their diffusion behavior reflect the influence of the self-organized order of the system.

Controlled structuring of binary hard-disk mixtures via a periodic, external potential.

Ordering phenomena on surfaces or in monolayers can be successfully studied by model systems as binary hard-disk mixtures, the influence of a substrate being modeled by an external potential. For the field-free case the thermodynamic stability of space-filling lattice structures for binary hard-disk mixtures is studied by Monte Carlo computer simulations. As these structures prove to be thermodynamically stable only in high pressure environments, the phase behavior of an equimolar binary mixture with a diameter ratio of sigma_{B}/sigma_{A}=0.414 exposed to an external, one-dimensional, periodic potential is analyzed in detail. The underlying ordering mechanisms and the resulting order differ considerably, depending on which components of the mixture interact with the external potential. The simulations show that slight deviations in the concentration of large particles x_{A} or the diameter ratio sigma_{B}/sigma_{A} have no impact on the occurrence of the various field-induced phenomena as long as the mixture stays in the relevant regime of the packing fraction eta . Furthermore the importance of the commensurability of the external potential to the S1(AB) square lattice for the occurrence of the induced ordering is discussed.

Nonlocal elastic compliance for soft solids: theory, simulations, and experiments.

The nonlocal elastic response function is crucial for understanding many properties of soft solids. This may be obtained by measuring strain-strain autocorrelation functions. We use computer simulations as well as video microscopy data of superparamagnetic colloids to obtain these correlations for two-dimensional triangular solids. Elastic constants and elastic correlation lengths are extracted by analyzing the correlation functions. We show that to explain our observations displacement fluctuations in a soft solid need to contain affine (strain) as well as nonaffine components.

Ordering of two-dimensional crystals confined in strips of finite width.

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential proportional, variantr;{-12} in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D ) depends very sensitively on the precise boundary conditions at the two "walls" providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-)long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y direction along the walls then crosses over from the logarithmic increase (characteristic for d=2 ) to a linear increase with n (characteristic for d=1 ). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising and XY models is made.

Layer reduction in driven 2D-colloidal systems through microchannels.

The transport behavior of a system of gravitationally driven superparamagnetic colloidal particles is investigated. The motion of the particles through a narrow channel is governed by magnetic dipole interactions, and a layered structure forms parallel to the walls. The arrangement of the particles is perturbed by diffusion and the motion induced by gravity leading to a density gradient along the channel. Our main result is the reduction of the number of layers. Experiments and Brownian dynamics simulations show that this occurs due to the density gradient along the channel.

Lack of long-range order in confined two-dimensional model colloidal crystals.

We investigate the nature of the ordered phase for a model of colloidal particles confined within a quasi-one-dimensional (Q1D) strip between two parallel boundaries, or walls, separated a distance D in two dimensions (2D). Using Monte Carlo simulations we find that at densities typical of the bulk 2D triangular solid the order in the D1D strip is determined by the nature of the boundaries. While the order is enhanced for a suitably corrugated boundary potential, for a uniformly repulsive smooth boundary potential ordering normal to the walls is enhanced ("layering"), but destroyed parallel to the wall.

Quantum corrections for the liquid-gas transition of Lennard-Jones particles in two dimensions.

The quantum corrections in first-order perturbation theory are semiquantitatively reproduced in the low temperature behavior of the liquid-gas coexistence curve of the simulations-at least for reduced masses down to m(*)=50.

Elastic properties of 2D colloidal crystals from video microscopy.

Elastic constants of two-dimensional (2D) colloidal crystals are determined by measuring strain fluctuations induced by Brownian motion of particles. Paramagnetic colloids confined to an air-water interface of a pendant drop are crystallized under the action of a magnetic field, which is applied perpendicular to the 2D layer. Using video microscopy and digital image processing we measure fluctuations of the microscopic strain obtained from random displacements of the colloidal particles from their mean (reference) positions. From these we calculate system-size dependent elastic constants, which are extrapolated using finite-size scaling to obtain their values in the thermodynamic limit. The data are found to agree rather well with zero-temperature calculations.

Phase transitions and quantum effects in pore condensates: a path integral Monte Carlo study.

Lennard-Jones condensates in cylindrical pores are studied by path integral Monte Carlo simulations with particular emphasis on phase transitions and quantum effects. The pore diameter effect and the influence of the interaction strength between the cylinder wall and the adsorbate particles on the structures and the location of the phase boundaries is studied and the quantum effect on the phase diagram is quantified by path integral Monte Carlo simulations. In case of strong wall-particle interactions good qualitative agreement with recent experimental results for the freezing of Ar-pore condensates is found. Meniscus structures in the solid phase are obtained as well as unexpected condensate structures for the system with the lighter Ne-particles due to quantum delocalization effects. The quantum effect on the freezing temperature can be as large as 10% in these systems.

Phase transitions of soft disks in external periodic potentials: a Monte Carlo study.

The nature of freezing and melting transitions for a system of model colloids interacting via the Derjaguin, Landau, Verwey, and Overbeek potential in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling analyses of various thermodynamic quantities, such as the order parameter, its cumulants, etc., are used to map the phase diagram of the system for various values of the reduced screening length kappaa(s) and the amplitude of the external potential. We find clear indication of a reentrant liquid phase over a significant region of the parameter space. Our simulations therefore show that the system of soft disks behaves in a fashion similar to charge stabilized colloids, which are known to undergo an initial freezing, followed by a remelting transition as the amplitude of the imposed, modulating field produced by crossed laser beams is steadily increased. The detailed analysis of our data shows several features consistent with a recent dislocation unbinding theory of laser induced melting.

Phase transitions of hard disks in external periodic potentials: a Monte Carlo study.

The nature of freezing and melting transitions for a system of hard disks in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling analysis of various thermodynamic quantities like the order parameter, its cumulants, etc., are used to map the phase diagram of the system for various values of the density and the amplitude of the external potential. We find clear indication of a reentrant liquid phase over a significant region of the parameter space. Our simulations therefore show that the system of hard disks behaves in a fashion similar to charge-stabilized colloids that are known to undergo an initial freezing, followed by a remelting transition as the amplitude of the imposed, modulating field produced by crossed laser beams is steadily increased. Detailed analysis of our data shows several features consistent with a recent dislocation unbinding theory of laser induced melting.

Elastic moduli, dislocation core energy, and melting of hard disks in two dimensions

Elastic moduli and dislocation core energy of the triangular solid of hard disks of diameter sigma are obtained in the limit of vanishing dislocation-antidislocation pair density, from Monte Carlo simulations that incorporate a constraint, namely that all moves altering the local connectivity away from that of the ideal triangular lattice are rejected. In this limit we show that the solid is stable against all other fluctuations at least up to densities as low as rhosigma(2)=0.88. Our system does not show any phase transition so diverging correlation lengths leading to finite size effects and slow relaxations do not exist. The dislocation pair formation probability is estimated from the fraction of moves rejected due to the constraint which yields, in turn, the core energy E(c) and the (bare) dislocation fugacity y. Using these quantities, we check the relative validity of first order and Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting scenarios and obtain numerical estimates of the typical expected transition densities and pressures. We conclude that a KTHNY transition from the solid to a hexatic phase preempts the solid to liquid first order transition in this system albeit by a very small margin, easily masked by crossover effects in unconstrained "brute- force" simulations with a small number of particles.

Elastic constants from microscopic strain fluctuations

Fluctuations of the instantaneous local Lagrangian strain epsilon(ij)(r,t), measured with respect to a static "reference" lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse-grained by averaging them within subsystems (of size L(b)) of a system (of total size L) in the canonical ensemble. Using a simple finite size scaling theory we predict the behavior of the fluctuations as a function of L(b)/L and extract elastic constants of the system in the thermodynamic limit at nonzero temperature. Our method is simple to implement, efficient, and general enough to be able to handle a wide class of model systems, including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of "hard" and "soft" disk triangular solids in two dimensions from Monte Carlo and molecular dynamics simulations. We compare our results with those from earlier simulations and theory.