Abstract: Thermal fluctuations of the order parameter in an ultrathin triangular-shaped superconducting structure are studied near Tc, in zero applied field. We find that the order parameter is prone to much larger fluctuations in the corners of the structure as compared to its interior. This geometry-induced localization of thermal fluctuations is attributed to the fact that condensate confinement in the corners is characterized by a lower effective dimensionality, which favors stronger fluctuations.

Abstract: We analyze theoretically and experimentally vortex configurations in mesoscopic superconducting squares. Our theoretical approach is based on the analytical solution of the London equation using Green's-function method. The potential-energy landscape found for each vortex configuration is then used in Langevin-type molecular-dynamics simulations to obtain stable vortex configurations. Metastable states and transitions between them and the ground state are analyzed. We present our results of the first direct visualization of vortex patterns in micrometer-sized Nb squares, using the Bitter decoration technique. We show that the filling rules for vortices in squares with increasing applied magnetic field can be formulated, although in a different manner than in disks, in terms of formation of vortex “shells”.

Abstract: Similar to the spontaneous formation of colonies of bacteria, flocks of birds, or schools of fish, “living crystals” can be formed by artificial self-propelled particles such as Janus colloids. Unlike usual solids, these “crystals” are far from thermodynamic equilibrium. They fluctuate in time forming a crystalline structure, breaking apart and re-forming again. We propose a method to stabilize living crystals by applying a weak confinement potential that does not suppress the ability of the particles to perform self-propelled motion, but it stabilizes the structure and shape of the dynamical clusters. This gives rise to such configurations of living crystals as “living shells” formed by Janus colloids. Moreover, the shape of the stable living clusters can be controlled by tuning the potential strength. Our proposal can be verified experimentally with either artificial microswimmers such as Janus colloids, or with living active matter.

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: The pattern formation of the vortex states with non-monotonic inter-vortex interaction is investigated. Our applied model has a short-range repulsive (r < r(c)) and long-range attractive (r > r(c)) potential. We numerically calculate the stable states using molecular-dynamics simulations. The obtained vortex patterns are comparable with the vortices states in low kappa type-II superconductors and recently discovered "type-1.5'' superconductors. We also analyze the nearest neighbor distribution of the obtained patterns. (C) 2012 Published by Elsevier B.V.

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.