Abstract: We show that in presence of an applied external field the two-component order parameter superconductor falls in two categories of ground states, namely, in the traditional Abrikosov ground state or in a new ground state fitted to describe a superconducting layer with texture, that is, patched regions separated by a phase difference of pi. The existence of these two kinds of ground states follows from the sole assumption that the total supercurrent is the sum of the two individual supercurrents and is independent of any consideration about the free energy expansion. Uniquely defined relations between the current density and the superfluid density hold for these two ground states, which also determine the magnetization in terms of average values of the order parameters. Because these ground-state conditions are also Bogomolny equations we construct the free energy for the two-component superconductor which admits the Bogomolny solution at a special coupling value. Copyright (C) EPLA, 2010

Abstract: We investigate a scattering of electron which is injected individually into an empty ballistic channel containing a cavity that is Coulomb coupled to a quantum ring charged with a single electron. We solve the time-dependent Schrödinger equation for the electron pair with an exact account for the electron-electron correlation. Absorption of energy and angular momentum by the quantum ring is not an even function of the external magnetic field. As a consequence we find that the electron backscattering probability is asymmetric in the magnetic field and thus violates Onsager symmetry.

Abstract: Triangular-shaped mesoscopic superconductors are consistent with the symmetry of the Abrikosov vortex lattice resulting in a high stability of vortex patterns for commensurate vorticities. However, for non-commensurate vorticities, vortex configurations in triangles are not compatible with the sample shape. Here we present the first direct observation of vortex configurations in ìm-sized niobium triangles using the Bitter decoration technique, and we analyze the vortex states in triangles by analytically solving the London equations and performing molecular-dynamics simulations. We found that filling rules with increasing vorticity can be formulated for triangles in a similar way as for mesoscopic disks where vortices form shells.

Abstract: Recently it was found that bilayer graphene may exhibit regions with and without van der Waals coupling between the two layers. We show that such structures can exhibit a strong layer selectivity when current flows through the coupled region and that this selectivity can be tuned by means of electrostatic gating. Analysing how this effect depends on the type of bilayer stacking, the potential on the gates and the smoothness of the boundary between the coupled and decoupled regions, we show that nearly perfect layer selectivity is achievable in these systems. This effect can be further used to realise a tunable layer switch.

Abstract: Static and dynamic properties of superconducting vortices in a superconducting stripe with a periodic array of weakly-superconducting (or normal metal) regions are studied in the presence of external magnetic and electric fields. The time-dependent Ginzburg-Landau theory is used to describe the electronic transport, where the anisotropy is included through the spatially-dependent critical temperature T-c. Superconducting vortices penetrating into the weak-superconducting region with smaller T-c are more mobile than the ones in the strong superconducting regions. We observe periodic entrance and exit of vortices which reside in the weak link for some short interval. The mobility of the weakly-pinned vortices can be reduced by increasing the uniform applied magnetic field leading to distinct features in the voltage vs. magnetic field response of the system.

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: Based on the metastable electron-pair energy band in a two-dimensional (2D) periodic potential obtained previously by Hai and Castelano [J. Phys.: Condens. Matter 26, 115502 (2014)], we present in this work a Hamiltonian of many electrons consisting of single electrons and electron pairs in the 2D system. The electron-pair states are metastable of energies higher than those of the single-electron states at low electron density. We assume two different scenarios for the single-electron band. When it is considered as the lowest conduction band of a crystal, we compare the obtained Hamiltonian with the phenomenological model Hamiltonian of a boson-fermion mixture proposed by Friedberg and Lee [Phys. Rev. B 40, 6745 (1989)]. Single-electron-electron-pair and electron-pair-electron-pair interaction terms appear in our Hamiltonian and the interaction potentials can be determined from the electron-electron Coulomb interactions. When we consider the single-electron band as the highest valence band of a crystal, we show that holes in this valence band are important for stabilization of the electron-pair states in the system.

Abstract: The angular and radial melting properties of two-dimensional classical systems consisting of different types of particles confined in a parabolic trap are studied through modified Monte Carlo simulations. A universal behavior of the angular melting process is found, which occurs in multiple steps due to shell depended melting temperatures. The melting sequence of the different shells is determined by two major factors: (1) the confinement strength which each shell is subjected to, and (2) the specific structure of each shell. Further, a continuous radial disordering of the particle types forming a single circular shell is found and analyzed. This phenomenon has never been observed before in two-dimensional mono-dispersive systems. This continuous radial disordering results from the high energy barrier between different particle types in multi-species systems.

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: We present an investigation of the orientations and positions of tubular fullerene molecules (C90, ..., C200) encapsulated in single-walled carbon nanotubes (SWCNT), a series of so-called fullerene nanopeapods. We find that increasing the tube radius leads to the following succession of energetically stable regimes: (1) lying molecules positioned on the tube's long axis; (2) tilted molecules on the tube's long axis; and (3) lying molecules shifted away from the tube's long axis. As opposed to C70 and C80 molecules encapsulated in a SWCNT, standing orientations do not develop. Our results are relevant for the possible application of molecular-orientation-dependent electronic properties of fullerene nanopeapods, and also for the interpretation of future experiments on double-walled carbon nanotube formation by annealing fullerene peapod systems.

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: Few-electron systems confined in two-dimensional parabolic quantum dots at high magnetic fields are studied by the Hartree-Fock (HF) and exact diagoiialization methods. A generalized multicenter Gaussian basis is proposed in the HF method. A comparison of the HF and exact, results allows as to discuss the relevance of the symmetry of the charge density distribution for the accuracy of the HF method. It is shown that the energy estimates obtained with the broken-symmetry HF wave functions become exact in the infinite magnetic-field limit. In this limit the charge density of the broken-symmetry solution call be identified with the classical charge distribution.