Hysteresis and reentrant melting of a self-organized system of classical particles confined in a parabolic trap

The melting of a self-organized system composed of classical particles confined in a two-dimensional parabolic trap and interacting through a potential with a short-range attractive part and a long-range repulsive potential is studied. Different behaviors of the melting temperature are found depending on the strength (B) of the attractive part of the interparticle potential. The melting of a system consisting of small bubbles takes place through a two-step melting process. A reentrant behavior and a thermally induced structural phase transition are observed in a small region of the (B,kappa) space. A hysteresis effect in the configuration of the particles is observed as a function of temperature. This is a consequence of the presence of a potential barrier between different configurations of the system.

Pinning-induced formation of vortex clusters and giant vortices in mesoscopic superconducting disks

Merged, or giant, multiquanta vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualize vortices in small Nb disks with varying degrees of disorder, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.

Two-dimensional binary clusters in a hard-wall trap: Structural and spectral properties

Within the Monte Carlo formalism supplemented by the modified Newton-Raphson optimization technique, we investigated structural and dynamical properties of two-dimensional binary clusters confined in an external hard-wall potential. Two species of differently charged classical particles, interacting through the repulsive Coulomb force are confined in the cluster. Subtle changes in the energy landscape and the stable cluster configurations are investigated as a function of the total number of particles and the relative number of each of the two particle species. The excitation spectrum and the normal modes corresponding to the ground-state configuration of the system are discussed, and the lowest nonzero eigenfrequency as a measure of the stability of the cluster is analyzed. The influence of the particle mass on the eigenfrequencies and eigenmodes are studied, i.e., we study a binary system of particles with different charge and different mass. Several unique features distinct from a monodisperse system are obtained.

Melting transitions in isotropically confined three-dimensional small Coulomb clusters

Molecular dynamic simulations are performed to investigate the melting process of small three-dimensional clusters (i.e., systems with one and two shells) of classical charged particles trapped in an isotropic parabolic potential. The confined particles interact through a repulsive potential. We find that the ground-state configurations for systems with N=6 , 12, 13, and 38 particles interacting through a Coulomb potential are magic clusters. Such magic clusters have an octahedral or icosahedral symmetry and are found to have a large stability against intrashell diffusion leading to an intershell melting transition prior to the intrashell and radial melting process. For systems with two shells a local radial melting of subshells is found at low temperatures resulting in a structural transition leading to an increased symmetry of the ordered system. Using Lindemann's criterion the different melting temperatures are determined and the influence of the screening of the interparticle interaction was investigated. A normal mode analysis is performed and some of the normal modes are found to be determinantal for the melting process.

New Andreev-type states in superconducting nanowires

Superconducting nanowires can exhibit a spatially inhomogeneous pair condensate that leads to the formation of new Andreev-type states. Such states are mainly located beyond the regions where the order parameter is enhanced, and no normal-superconducting contact or external magnetic field is needed for their formation. Our numerical self-consistent solutions of the Bogoliubov-de Gennes equations for cylindrical nanowires, in the clean limit, demonstrate that these new Andreev-type states decrease the ratio of the energy gap to the critical temperature as compared to its bulk value. The low-lying excitations in a clean superconducting nanowire are these new Andreev-type states induced by quantum confinement of the electrons in the transverse direction.

Nonmonotonic field dependence of damping and reappearance of Rabi oscillations in quantum dots

The dynamics of strongly confined laser driven semiconductor quantum dots coupled to phonons is studied theoretically by calculating the time evolution of the reduced density matrix using a numerical path integral method. We explore the cases of long pulses, strong dot-phonon and dot-laser coupling, and high temperatures, which, up to now, have been inaccessible. We find that the phonon-induced damping of Rabi rotations is a nonmonotonic function of the laser field that is increasing at low fields and decreasing at high fields. This results in a reappearance of Rabi rotations at high fields. This phenomenon is of a general nature which occurs for all temperatures and carrier-phonon coupling strengths.

Electric-field manipulation of spin states in confined non-magnetic/magnetic heterostructures

The energy spectrum and states of an electron in a non-magnetic/magnetic heterostructure placed between two materials (e.g. oxides) acting as barriers is studied in the presence of a magnetic field perpendicular or parallel to the well. A potential step is formed at the interface between the non-magnetic and magnetic material in the presence of a magnetic field since spin-up electrons see a barrier whereas the spin-down ones see a well. A rich band structure is obtained which can be tuned by a perpendicular electric field. Numerical results are presented for a ZnSe/Zn(1-x)Mn(x)Se heterostructure and their pertinence to spin-polarized transport is pointed out.

Tunable quantum dots in bilayer graphene

We demonstrate theoretically that quantum dots in bilayers of graphene can be realized. A position-dependent doping breaks the equivalence between the upper and lower layer and lifts the degeneracy of the positive and negative momentum states of the dot. Numerical results show the simultaneous presence of electron and hole confined states for certain doping profiles and a remarkable angular momentum dependence of the quantum dot spectrum, which is in sharp contrast with that for conventional semiconductor quantum dots. We predict that the optical spectrum will consist of a series of nonequidistant peaks.

Dynamics of scattering on a classical two-dimensional artificial atom

A classical two-dimensional (2D) model for an artificial atom is used to make a numerical "exact" study of elastic and nonelastic scattering. Interesting differences in the scattering angle distribution between this model and the well-known Rutherford scattering are found in the small energy and/or small impact parameter scattering regime. For scattering off a classical 2D hydrogen atom different phenomena such as ionization, exchange of particles, and inelastic scattering can occur. A scattering regime diagram is constructed as function of the impact parameter (b) and the initial velocity (v) of the incoming particle. In a small regime of the (b,v) space the system exhibits chaos, which is studied in more detail. Analytic expressions for the scattering angle are given in the high impact parameter asymptotic limit.

Symmetric and asymmetric vortex-antivortex molecules in a fourfold superconducting geometry

In submicron superconducting squares in a homogeneous magnetic field, Ginzburg-Landau theory may admit solutions of the vortex-antivortex type, conforming to the symmetry of the sample [L. F. Chibotaru, Nature (London) 408, 833 (2000)10.1038/35048521]. Here we show that these fascinating, but never experimentally observed states, can be enforced by artificial fourfold pinning, with their diagnostic features enhanced by orders of magnitude. The second-order nucleation of vortex-antivortex molecules can be driven by either temperature or an applied magnetic field, with stable asymmetric vortex-antivortex equilibria found on its path.

Inhomogeneous melting in anisotropically confined two-dimensional clusters

Molecular dynamic simulations are performed to investigate the melting process of two-dimensional clusters of classical charged particles trapped in an anisotropic parabolic potential. The confined particles interact through a repulsive potential. We find that the eccentricity of the confinement potential strongly affects the melting pattern of such clusters. Increasing the eccentricity of the confinement potential drives the system through three different melting regimes. Inhomogeneous melting is the typical melting process for anisotropically confined clusters and its appearance in small systems occurs in a distinct form called here internal intershell melting. The latter involves only particles in the center of the cluster while particles on the far left and right of the cluster are still ordered having a much higher melting temperature. Using the Lindemann's criterion the melting temperatures are determined as a function of the different parameters. The internal intershell melting process is found for both long-range (i.e., logarithmic) and short-range (i.e., screened Coulomb) interparticle interaction. Decreasing the range of the interparticle interaction increases the eccentricity of the confinement potential for which internal intershell melting can occur.

Novel commensurability effects in superconducting films with antidot arrays

Vortex configurations in superconducting films with regular arrays of antidots (holes) are calculated within the nonlinear Ginzburg-Landau theory. In addition to the well-established matching phenomena, we predict (i) the nucleation of giant-vortex states between the antidots, (ii) the combination of giant- and multivortices at rational matching fields, and (iii) for particular values of the vorticity, symmetry imposed creation of vortex-antivortex configurations.

Exciton states in cylindrical nanowires

The exciton ground state and excited state energies are calculated for a model system of an infinitely long cylindrical wire. The effective Coulomb potential between the electron and the hole is studied as function of the wire radius. Within the adiabatic approximation, we obtain 'exact' numerical results for the effective exciton potential and the lowest exciton energy levels which are fitted to simple analytical expressions. Furthermore, we investigated the influence of a magnetic field parallel to the nanowire on the effective potential and the exciton energy.

Spectrum of classical two-dimensional Coulomb clusters

The frequency spectrum of a system of classical charged particles interacting through a Coulomb repulsive potential and which are confined in a two-dimensional parabolic trap is studied. It is shown that, apart from the well-known center-of-mass and breathing modes, which are independent of the number of particles in the cluster, there are more "universal" modes whose frequencies depend only slightly on the number of particles. To understand these modes the spectrum of excitations as a function of the number of particles is compared with the spectrum obtained in the hydrodynamic approach. The modes are classified according to their averaged vorticity and it is shown that these "universal" modes have the smallest vorticity and follow the hydrodynamic behavior.

Melting and evaporation in classical two-dimensional clusters confined by a Coulomb potential

The thermal properties of a two-dimensional classical cluster of negatively charged particles bound by a punctual positive charge are presented. The melting phenomenon is analyzed and the features which characterize such a solid-liquid transition are highlighted. We found that the presence of metastable states strongly modifies the melting scenario, and that the melting temperature of the system is determined by the height of the saddle point energy separating the ground state and the metastable state. Due to the particular type of confinement potential considered in this paper, we also found that, at sufficiently large temperature, the cluster can become thermally ionized.

Structure and spectrum of anisotropically confined two-dimensional clusters with logarithmic interaction

We studied the structural and spectral properties of a classical system consisting of a finite number of particles, moving in two dimensions, and interacting through a repulsive logarithmic potential and held together by an anisotropic harmonic potential. Increasing the anisotropy of the confinement potential can drive the system from a two-dimensional (2D) to a one-dimensional (1D) configuration. This change occurs through a sequence of structural transitions of first and second order which are reflected in the normal mode frequencies. Our results of the ground state configurations are compared with recent experiments and we obtained a satisfactory agreement. The transition from the 1D line structure to the 2D structure occurs through a zigzag transition which is of second order. We found analytical expressions for the eigenfrequencies before the zigzag transition, which allowed us to obtain an analytical expression for the anisotropy parameter at which the zigzag transition occurs as a function of the number of particles in the system.

Mesoscopic field and current compensator based on a hybrid superconductor-ferromagnet structure

A rather general enhancement of superconductivity is demonstrated in a hybrid structure consisting of a submicron superconducting (SC) sample combined with an in-plane ferromagnet (FM). The superconducting state resists much higher applied magnetic fields for both perpendicular polarities, as the applied field is screened by the FM. In addition, FM induces (in the perpendicular direction to its moment) two opposite currents in the SC plane, under and aside the magnet, respectively. Because of the compensation effects, superconductivity persists up to higher applied currents. With increasing current, the sample undergoes SC-"resistive"-normal state transitions through a mixture of vortex-antivortex and phase-slip phenomena.

Structure, normal mode spectra, and mixing of a binary system of charged particles confined in a parabolic trap

We study the mixing of two different kinds of particles, having different charge and/or mass, interacting through a pure Coulomb potential, and confined in a parabolic trap. The structure of the cluster and its normal mode spectrum are analyzed as a function of the ratio of the charges (mass ratio) of the two types of particles. We show that particles are not always arranged in a shell structure. Mixing of the particles goes hand in hand with a large number of metastable states. The normal modes of the system are obtained, and we find that some of the special modes can be tuned by varying the ratio between the charges (masses) of the two species. The degree of mixing of the two type of particles is summarized in a phase diagram, and an order parameter that describes quantitatively the mixing between particles is defined.

Vortex-antivortex nucleation in magnetically nanotextured superconductors: magnetic-field-driven and thermal scenarios

Within the Ginzburg-Landau formalism, we predict two novel mechanisms of vortex-antivortex nucleation in a magnetically nanostructured superconductor. Although counterintuitive, nucleation of vortex-antivortex pairs can be activated in a superconducting (SC) film covered by arrays of submicron ferromagnets (FMs) when exposed to an external homogeneous magnetic field. In another scenario, we predict the thermal induction of vortex-antivortex configurations in SC-FM samples. This phenomenon leads to a new type of Little-Parks oscillations of the FM magnetization-temperature phase boundary of the SC film.

Bubble, stripe, and ring phases in a two-dimensional cluster with competing interactions

A system of classical charged particles confined in a two-dimensional trap and interacting through a competing short-range attraction and long-range repulsion potential is studied. The structure of the system strongly depends on the interaction range of the short-range attraction potential and the total number of particles. Depending on the appropriate choice of parameters for the attractive potential, the particles organize themselves in bubbles, stripe phases, and ringlike configurations, or combinations of both of them. Detailed phase diagrams are presented for systems consisting of N=2 up to N=6 particles. General rules are derived for the different subsequent transitions between those configurations and how the ground state configuration of a large system can be deduced from the one of a small number of particles.

Multistep radial melting in small two-dimensional classical clusters

We report on a molecular dynamics study of small classical two-dimensional clusters with ringlike configurations. We focus on the particles motion at low temperatures before the radial and angular melting sets in. It is shown that in magic number configurations a local radial melting of subshells occur, which is related to the intershell rotation.

Structural phase transitions and unusual melting behavior in a classical two-dimensional Coulomb bound cluster

The melting properties of a cluster with N equally charged particles confined by a Coulomb potential are studied. The system exhibits a structural phase transition before it melts. The melting process is not dominated by the usual thermal hops between stable states. We also show that the symmetry of the ground state configuration is a dominant factor in determining the melting temperature and that more confined particles in the cluster do not necessarily have a higher melting temperature.

Vortex-antivortex lattices in superconducting films with magnetic pinning arrays

Novel vortex structures are found when a thin superconducting (SC) film is covered with a lattice of out-of-plane magnetized magnetic dots (MDs). The stray magnetic field of the dots confines the vortices to the MD regions, surrounded by antivortices which "crystallize" into regular lattices. First- and second-order transitions are found as the magnetic array is made sparser or MD magnetization larger. For sparse MD arrays fractional vortex-antivortex states are formed, where the crystal symmetry is combined with a nonuniform "charge" distribution. We demonstrate that due to the (anti)vortices and the supercurrents induced by the MDs, the critical current of the sample actually increases if exposed to a homogeneous external magnetic field, contrary to conventional SC behavior.

Experimental evidence for giant vortex states in a mesoscopic superconducting disk

The response of a mesoscopic superconducting disk to perpendicular magnetic fields is studied by using the multiple-small-tunnel-junction method, in which transport properties of several small tunnel junctions attached to the disk are measured simultaneously. This allows us to make the first experimental distinction between the giant vortex states and multivortex states. Moreover, we experimentally find a magnetic-field induced rearrangement and combination of vortices. The experimental results are well reproduced in numerical results based on the nonlinear Ginzburg-Landau theory.