Abstract: The influence of random pinning on the vortex dynamics in a periodic square potential under an external drive is investigated. Using numerical experiments and theoretical approach, we found several dynamical regimes of vortex motion that are different from the ones for a regular pinning potential. Vortex transfer is controlled by kinks and antikinks, which either pre-exist in the system or appear spontaneously in pairs and then propagate. When kinks and antikinks collide, they annihilate. We provide clear physical interpretations of the observed features.

Abstract: When floating on a two-dimensional surface of superfluid He-4, electrons arrange themselves in two-dimensional crystalline structure known as Wigner crystal. In channels, the boundaries interfere the crystalline order and in case of very narrow channels one observes a quasi-one-dimensional (quasi-1D) Wigner crystal formed by just a few rows of electrons and, ultimately, one row in the “quantum wire” regime. Recently, the “quantum wire” regime was accessed experimentally [D.G. Rees, H. Totsuji, K. Kono, Phys. Rev. Lett. 108, 176801 (2012)] resulting in unusual transport phenomena such as, e.g., oscillations in the electron conductance. Using molecular dynamics simulations, we study the nonlinear transport of electrons in channels with various types of constrictions: single and multiple symmetric and asymmetric geometrical constrictions with varying width and length, and saddle-point-type potentials with varying gate voltage. In particular, we analyze the average particle velocity of the particles and the corresponding electron current versus the driving force or the gate voltage. We have revealed a significant difference in the dynamics for long and short constrictions: The oscillations of the average velocity of the particles for the systems with short constrictions exhibit a clear correlation with the transitions between the states with different numbers of rows of particles; on the other hand, for the systems with longer constrictions these oscillations are suppressed. The obtained results qualitatively agree with the experimental observations. Next, we propose a FET-like structure that consists of a channel with asymmetric constrictions. We show that applying a transverse bias results either in increase of the average particle velocity or in its suppression thus allowing a flexible control tool over the electron transport. The advantage of the asymmetric FET is that it does not have a gate and it allows an easy control of relatively large electron flow. Furthermore, the asymmetric device can be used for rectification of an ac-driven electron flow. Our results bring important insights into the dynamics of electrons floating on the surface of superfluid He-4 in channels with constrictions and allow the effective control over the electron transport.

Abstract: Electrons on liquid helium can form different phases depending on density, and temperature. Also the electron-ripplon coupling strength influences the phase diagram, through the formation of so-called “ripplonic polarons”, that change how electrons are localized, and that shifts the transition between the Wigner solid and the liquid phase. We use an all-coupling, finite-temperature variational method to study the formation of a ripplopolaron Wigner solid on a liquid helium film for different regimes of the electron-ripplon coupling strength. In addition to the three known phases of the ripplopolaron system (electron Wigner solid, polaron Wigner solid, and electron fluid), we define and identify a fourth distinct phase, the ripplopolaron liquid. We analyse the transitions between these four phases and calculate the corresponding phase diagrams. This reveals a reentrant melting of the electron solid as a function of temperature. The calculated regions of existence of the Wigner solid are in agreement with recent experimental data.

Abstract: Here we summarize results from our study of the critical depinning current J(c) versus the applied magnetic flux Phi, for: (i) quasiperiodic (QP) one-dimensional (1D) chains and (ii) 2D arrays of pinning centers placed on the nodes of a five-fold Penrose lattice. In 1D QP chains, the peaks in J(c)(Phi) are determined by a sequence of harmonics of the long and short segments of the chain. The critical current J(c)(Phi) has a remarkable self-similarity. In 2D QP pinning arrays, we predict analytically and numerically the main features of J(c)(Phi), and demonstrate that the Penrose lattice of pinning sites provides an enormous enhancement of J(c)(Phi), even compared to triangular and random pinning site arrays. This huge increase in J(c)(Phi) could be useful for applications. (c) 2005 Elsevier B.V. All rights reserved.

Abstract: Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.

Abstract: Microscopic self-propelled swimmers capable of autonomous navigation through complex environments provide appealing opportunities for localization, pick-up and delivery of micro and nanoscopic objects. Inspired by motile cells and bacteria, man-made microswimmers have been fabricated, and their motion in patterned surroundings has been experimentally studied. We propose to use self-driven artificial microswimmers for the separation of binary mixtures of colloids. We revealed different regimes of separation, including one with a velocity inversion. Our findings could be of use for various biological and medical applications.

Abstract: We study theoretically the simultaneous effect of regular and random pinning potentials on the vortex lattice structure at filling factor of 1. This structure is determined by a competition between the square symmetry of regular pinning array, by the intervortex interaction favoring a triangular symmetry, and by the randomness trying to depin vortices from their regular positions. Both analytical and molecular-dynamics approaches are used. We construct a phase diagram of the system in the plane of regular and random pinning strengths and determine typical vortex lattice defects appearing in the system due to the disorder. We find that the total disordering of the vortex lattice can occur either in one step or in two steps. For instance, in the limit of weak pinning, a square lattice of pinned vortices is destroyed in two steps. First, elastic chains of depinned vortices appear in the film; but the vortex lattice as a whole remains still pinned by the underlying square array of regular pinning sites. These chains are composed into fractal-like structures. In a second step, domains of totally depinned vortices are generated and the vortex lattice depins from regular array.