Structure, melting, and potential barriers in mesoscopic clusters of repulsive particles

This paper discusses two-dimensional mesoscopic clusters of particles that repel according to dipole, Coulomb, and logarithmic laws and are confined by an external parabolic potential. These models describe a number of physical systems, in particular, electrons in semiconductor structures or on a liquid-helium surface allowing for image forces, indirect excitons in coupled semi-conductor dots, and a small number of vortices in an island of a second-order superconductor or in superfluid helium. Two competing forms of ordering are detected in the particles in the mesoscopic clusters-the formation of a triangular lattice or of a shell structure. The temperature dependences of the potential energy, the mean-square radial and angular deviations, the radial and angular distributions of the particles, and the distribution of the particles over the local minima are studied. Melting in mesoscopic clusters occurs in two stages: at lower temperatures, there is orientation melting, from the frozen phase into a phase with rotational reorientation of “crystalline” shells with respect to each other; subsequently, a transition occurs in which the radial order disappears. Melting in dipole macroclusters occurs in a single stage. However, in Coulomb and logarithmic macroclusters, orientation melting occurs only for the outer pairs of shells. Orientation melting is also detected in three-dimensional Coulomb clusters. A connection is established between the character of the melting and the ratio of the energy barriers that describe the breakdown of the orientational and radial structure of a cluster. Zh. éksp. Teor. Fiz. 116, 2012–2037 (December 1999)     

Influence of the pinning of Abrikosov vortices on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure

The influence of surface-layer vortex pinning in a type-II superconductor on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure is analyzed. The pinning is assumed to be strong enough to prevent vortex displacement under the influence of the Lorentz force generated by the surface magnetostatic waves, so that the ground state of the superconductor is determined by the elastic properties of the vortex lattice and by pinning. In the given model the problem reduces to the analysis of the wave spectrum in the scattered field created by the disordered vortex surface layer. A calculation shows that the influence of this field on the surface magnetostatic-wave spectrum is slight and, hence, degradation of the shielding properties of the superconductor does not take place in the presence of strong vortex pinning (as opposed to the ferromagnet-ideal superconductor structure). Fiz. Tverd. Tela (St. Petersburg) 40, 32–35 (January 1998)     

Field theory of mesoscopic fluctuations in superconductor-normal-metal systems

Thermodynamic and transport properties of mesoscopic conductors are strongly influenced by the proximity of a superconductor: an interplay between the large scale quantum coherent wave functions in the normal mesoscopic and the superconducting region, respectively, leads to unusual mechanisms of quantum interference. These manifest themselves in both the mean and the mesoscopic fluctuation behaviour of superconductor-normal-metal (SN) hybrid systems being strikingly different from those of conventional mesoscopic systems. After reviewing some established theories of SN quantum interference phenomena, we introduce a new approach to the analysis of SN mesoscopic physics. Essentially, our formalism represents a unification of the quasi-classical formalism for describing mean properties of SN systems on the one hand, with more recent field theories of mesoscopic fluctuations on the other hand. Thus, by its very construction, the new approach is capable of exploring both averaged and fluctuation properties of SN systems on the same microscopic footing. As an example, the method is applied to the study of various characteristics of the single particle spectrum of SNS structures.     

Electron spectroscopy of objects for nanoelectronics

An electron-spectroscopic analysis is made of layered nanostructures and clusters at the surface and in the bulk of a solid. A new method of forming metal/insulator/semiconductor (superconductor) nanostructures is proposed based on ion-stimulated metal segregation effects at the surface of low-temperature gallium arsenide and a 123 high-temperature superconductor. The geometric parameters and electronic structure of these nano-objects are studied. It is shown that their electronic properties can be controllably varied in situ by acting on the surface. The dimensional transformation of the electronic properties of metal clusters is studied for clusters in the insulator SiO₂, in the superconductor LTMBE-GaAs, and on silicon and graphite surfaces. The nature of this transformation is clarified. A diagnostics for cluster ensembles is developed by which one can determine the parameters needed to describe singleelectron transport: the average number of atoms per cluster, the average distance between clusters and isolated atoms, and the chemical state of the atoms. Ensembles of silver clusters with specified parameters are obtained on a silicon surface. It is shown that these ensembles are potentially useful for developing single-electron devices. Zh. Tekh. Fiz. 69, 85–89 (September 1999)     

Long-range coherence and mesoscopic transport in N–S metallic structures

We review the mesoscopic transport in a diffusive proximity superconductor made of a normal metal (N) in metallic contact with a superconductor (S). The Andreev reflection of electrons on the N–S interface is responsible for the diffusion of electron pairs in N. Superconducting-like properties are induced in the normal metal. In particular, the conductivity of the N metal is locally enhanced by the proximity effect. A re-entrance of the metallic conductance occurs when all the energies involved (e.g. temperature and voltage) are small. The relevant characteristic energy is the Thouless energy which is divided by the diffusion time for an electron travelling throughout the sample. In loop-shaped devices, a 1 / T temperature-dependent oscillation of the magnetoresistance arises with a large amplitude from the long-range coherence of low-energy pairs.     

Distribution of the local magnetic field of the vortex lattice near the surface of an anisotropic superconductor in oblique external magnetic fields

The distribution of the magnetic field in the unit cell of the Abrikosov vortex lattice near the surface of a uniaxial, anisotropic, type-II superconductor in an oblique external magnetic field is determined on the basis of the London model for the cases in which the symmetry axis is perpendicular and parallel to the boundary of the superconductor. The distribution of the local magnetic field is obtained as a function of the distance from the surface of the superconductor and the inclination angle of the external field. It is shown for an YBaCuO high-T _c superconductor that the investigation of the distribution function of the local magnetic field as a function of the angle of the external magnetic field relative to the symmetry axis and to the surface of the superconductor can yield important information about the anisotropic properties of the superconductor. Fiz. Tverd. Tela (St. Petersburg) 39, 1935–1939 (November 1997)     

Stress state of a matrix and an inclusion consisting of a twisted multifilament superconductor with a normally-conducting core in the presence of an interaction of the longitudinal current with a transverse magnetic field

A study is made of the stress state arising in an infinite matrix into which is “potted” a long cylindrical inclusion consisting of a twisted multifilament composite superconductor with a core of normal metal as a result of the interaction of the longitudinal component of the transport current with a uniform external magnetic field. It is shown that the approximation of a homogeneous conductor with average elastic properties can be used to calculate the macroscopic stresses in a NbTi-Cu wire embedded in an epoxy matrix. Zh. Tekh. Fiz. 68, 39–42 (October 1998)     

Supercooling in a system of two superconductors

Supercooling in the transition of a type I superconductor to the superconducting state in contact with another superconductor whose critical temperature is higher has been measured. Using aluminum as a test material, it has been demonstrated that at temperatures below the critical temperature T _c and magnetic fields below the critical field H _c(T), aluminum remains in a metastable normal state, in spite of its contact with another superconductor. This means that it is not possible to generate a thermodynamic instability in a superconductor’s electronic system through the “proximity effect” with another superconductor whose critical temperature is higher. This experimental observation demonstrates a radical difference between surface superconductivity, which certainly generates instability in normal electronic states, and superconductivity induced by the proximity effect near a junction with another superconductor. Zh. éksp. Teor. Fiz. 112, 1119–1131 (September 1997)     

Longitudinal critical current in a ferrite-type-II superconductor structure

The effect of the interaction of Abrikosov vortices with the magnetization on the longitudinal vortical instability in a layered ferromagnet-type-II superconductor structure is analyzed. It is shown that in the vicinity of the orientational phase transition in the magnet, where the transverse magnetic susceptibility is large, the magnitude of the longitudinal critical current in the structure can be almost 1.5 times smaller than in the isolated superconductor. The reason for this is compensation of stray field sources outside the superconductor by “magnetic charges” arising from a jump in the transverse magnetization on the surface of the magnet. A structure is considered in which the thickness of the superconductor significantly exceeds the London penetration depth of the magnetic field and the wavelength of the critical mode. For this reason (in light of the absence of high-quality bulk high-temperature superconductors), to experimentally study the described phenomenon it is necessary to use conventional low-temperature superconductors. Fiz. Tverd. Tela (St. Petersburg) 39, 231–235 (February 1997)     

Shape of the magnetic resonance line in a thin film on the surface of an anisotropic superconductor

The shape of the EPR line in a thin (=λ/2, where λ is the London penetration depth of the magnetic field in the superconductor) paramagnetic film deposited on the surface of an anisotropic superconductor is calculated in an oblique magnetic field with allowance for the inhomogeneity of the local magnetic field of the Abrikosov vortex lattice. It is shown that, as the tilt angle of the external magnetic field is varied, the shape of the EPR line changes noticeably. This fact can give additional information about the superconductor parameters (the symmetry type of the vortex lattice and the anisotropy parameter of the superconductor). Fiz. Tverd. Tela (St. Petersburg) 41, 386–388 (March 1999)     

Surface electron scattering in d-wave superconductors

A theoretical model of a rough surface in a d-wave superconductor is studied for the general case of arbitrary strength of electron scattering by an impurity layer covering the surface. Boundary conditions for quasiclassical Eilenberger equations are derived at the interface between the impurity layer and the d-wave superconductor. The model is applied to the self-consistent calculation of the surface density of states and the critical current in d-wave Josephson junctions. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 242–246 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Decay of mesoscopically localized vibrations in porous materials

The low-temperature decay of a vibrational eigenstate of a crystalline mesoscopic particle surrounded by other such particles of approximately the same size is considered. The decay time is determined by the anharmonicity and the coupling between adjacent mesoscopic particles. Under some limiting conditions for particles of a typical size of 50 Å the decay time at low temperatures can be several milliseconds. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 51–56 (10 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Electrons and photons in mesoscopic structures: Quantum dots in a photonic crystal

The synthesis and properties of a photonic crystal doped with quantum dots are reported. The structure exhibits a two-stage self-organization of silica nanoparticles along with quantum confinement effects in semiconductor colloids. The interplay of electron and photon confinement results in controllable spontaneous emission from the mesoscopic structure. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 2, 131–135 (25 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Propagation of magnetostatic waves in a ferrite plus high-T c superconductor structure in the presence of transport current in the superconductor

A thin-film structure consisting of a ferrite and a high-T _c superconductor was used to investigate the effct of the transport current in the superconductor on the amplitude-frequency characteristic and dispersion of surface magnetostatic waves (MSWs) in a ferrite film. It was found that the nature of energy transfer between the MSWs and the superconducting film undergoes a significant change as the transport current is varied. In particular, in one of the current ranges, energy can be transferred both from the MSWs to the superconductor and back again, whereas in another range it can only be efficently transferred to the superconductor. Fiz. Tverd. Tela (St. Petersburg) 39, 2195–2202 (December 1997)     

Antivortices due to competing orbital and paramagnetic pair-breaking effects

Thermodynamically stable vortex—antivortex structures in a quasi-twodimensional superconductor in a tilted magnetic field are predicted. For this geometry, both orbital and spin pair-breaking effects exist, with their relative strength depending on the tilt angle θ. The spectrum of possible states contains the ordinary vortex state (for large θ) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state (for θ = 0) as limits. The quasi-classical equations are solved nearH _c2 for arbitrary θ and it is shown that stable states with co-existing vortices and antivortices exist in a small interval close to θ= 0. The results are compared with recent predictions of antivortices in mesoscopic samples.     

On the mechanism of dissipation in the internal Josephson effect in layered superconductors at low temperatures

The current-voltage characteristics (IVCs) of a layered superconductor with singlet d pairing at low temperatures are calculated in the internal Josephson effect (IJE) regime. Coherent electron tunneling between layers is assumed. A finite resistance of the superconductor in the resistive state arises because of quasiparticle transitions through the superconducting gap near nodes. Because of charge effects the interaction of the Josephson junctions formed by the layers does not lead to substantial differences in the shapes of different branches of the IVCs. The model describes the basic qualitative features of the effect in high-temperature superconductors for voltages which are low compared with the amplitude of the superconducting gap. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 516–521 (25 October 1999)     

Contribution of Andreev reflection to the increase in the resistance of the normal metal in a bimetallic N-S structure

We study the resistive properties of 3D normal-metal-superconductor systems in the pure mean-free-path limit l _N,S ≫ξ(T) (l _N,S are the mean free paths in the metals, and ξ is the coherence length) at liquid helium temperatures. In contrast to the situation where l≪ξ, which is common in experiments involving either sandwiches or mesoscopic samples, here the N-S system exhibits unusual temperature behavior that cannot be described by existing theories of boundary resistance. What is most remarkable is a rise in normal resistance in regions that do not incorporate the N-S boundary as the temperature decreases, with asymptotic behavior resembling that of the temperature curve of the gap of a superconductor in contact with a normal metal. We show that this effect, not observed earlier in 3D systems, is due to the nonequivalence of the cross sections of scattering by normal-metal impurities of electron and hole excitations in conditions of Andreev reflection. We also show that in standard measurements of the contribution of the N-S boundary lying between the test contacts, this effect is masked by accompanying effects, the proximity effect and the boundary resistance, whose estimate requires taking into account the presence on the N-S boundary of an electrostatic barrier of the Schottky type, a barrier that redistributes the probabilities of ordinary and Andreev reflections of quasiparticles in the nonequilibrium conditions due to current flow. Zh. éksp. Teor. Fiz. 113, 1064–1070 (March 1998)     

Current transport along the [001] axis of YBCO in low-temperature superconductor-normal metal-high-temperature superconductor heterostructures

The electrophysical properties of heterojunctions several microns in size, obtained by successive deposition of the metal-oxide high-temperature superconductor YBa₂Cu₃O_x, a normal metal Au, and the low-temperature superconductor Nb, were studied experimentally. Current flows in the [001] direction of the epitaxial YBa₂Cu₃O_x film. It is shown, by comparing the experimental data with existing theoretical calculations, that for the experimentally realizable transmittances (D̄=10⁻⁵–10⁻⁶) of the YBa₂Cu₃O_x—normal metal boundary the critical current of the entire heterostructure is low (of the order of the fluctuation current) because of a sharp change in the amplitude of the potential of the superconducting carriers at this boundary. The current-voltage characteristics of the heterostructure studied correspond to tunnel junctions consisting of a superconductor with type symmetry of the superconducting wave function and a normal metal. Zh. éksp. Teor. Fiz. 116, 2140–2149 (December 1999)     

Dynamic magnetic susceptibility of a superconductor with a relaxing magnetic moment

Within the framework of the diffusion approximation for the dynamic magnetic flux, a model is constructed for the dynamic magnetic susceptibility of a superconductor with a nonuniform and time-dependent magnetic field distribution in the sample. The possibility of appearance of peaks in the temperature (or frequency) dependence of χ″ in a structurally homogeneous superconducting sample in the presence of a magnetic-field-induced nonuniformity of the diffusion parameter is demonstrated. The character of the temporal evolution of the magnetic susceptibility during relaxation of the magnetic moment of the sample is predicted and its properties are investigated. Fiz. Tverd. Tela (St. Petersburg) 39, 811–815 (May 1997)