Mesoscopic Grains Research Articles

SuperConga: An open-source framework for mesoscopic superconductivity

We present SuperConga, an open-source framework for simulating equilibrium properties of unconventional and ballistic singlet superconductors, confined to two-dimensional (2D) mesoscopic grains in a perpendicular external magnetic field, at arbitrary low temperatures. It aims at being both fast and easy to use, enabling research without access to a computer cluster, and visualization in real-time with OpenGL. The core is written in C++ and CUDA, exploiting the embarrassingly parallel nature of the quasiclassical theory of superconductivity by utilizing the parallel computational power of modern graphics processing units. The framework self-consistently computes both the superconducting order-parameter and the induced vector potential and finds the current density, free energy, induced flux density, local density of states (LDOS), and the magnetic moment. A user-friendly Python frontend is provided, enabling simulation parameters to be defined via intuitive configuration files, or via the command-line interface, without requiring a deep understanding of implementation details. For example, complicated geometries can be created with relative ease. The framework ships with simple tools for analyzing and visualizing the results, including an interactive plotter for spectroscopy. An overview of the theory is presented, as well as examples showcasing the framework's capabilities and ease of use. The framework is free to download from https://gitlab.com/superconga/superconga, which also links to the extensive user manual, containing even more examples, tutorials, and guides. To demonstrate and benchmark SuperConga, we study the magnetostatics, thermodynamics, and spectroscopy of various phenomena. In particular, we study flux quantization in solenoids, vortex physics, surface Andreev bound-states, and a “phase crystal.” We compare our numeric results with analytics and present experimental observables, e.g., the magnetic moment and LDOS, measurable with, for example, scanning probes, STM, and magnetometry.

Preparation and characterization of palladium-doped titanium dioxide for solar cell applications

The syntheses of TiO2 and Pd/TiO2 nanoparticles were carried by hydrolysis of alkoxide precursors using the reverse micelles method using titanium tetrabutoxide and palladium acetylacetonate as precursor metals. The method was modified by precipitation with the addition of n-butanol and then washed with an ethanol/water solution at a ratio of 1:1. Morphological characterization was performed by scanning electron microscopy and structural by X-ray diffraction and spectroscopy of Raman scattering. Electrical characterization was performed by impedance spectroscopy and the optical energy gap was determined from transmittance measurements Tauc plot fittings. The material was characterized by a suspension of spherical nanoparticles on the order of 100 nm confirmed by Scanning electron microscopy analysis. They also presented good ionic conductivity as indicated by impedance spectroscopy. Raman spectroscopy showed a systematic frequency shift to the left together with peak broadening as the amount of palladium incorporated onto TiO2 increases, which is characteristic of mesoscopic grains. X-ray diffractograms were carried with washed and dried powder samples and showed a mixture of anatase and brookite phases, with anatase as the predominant one.

Enhancement of Hard Magnetic Properties in Fraktal-Like Nano and Mesoscopic Grains.

The paper refers to Monte Carlo magnetic simulations for fractal-like nano and mesoscopic grains. The analyzed objects differed in the size, surface development, magnetic anisotropy and the spin values attributed to the system nodes inside the fractal. Such an approach allowed us to determine their magnetization processes as well as optimization characteristics in the direction to enhancement of hard magnetic properties. As it was shown, the size effects depend on the chosen value of magnetic anisotropy. In the case of fractals with ultra-high coercivity, the decreasing of their size leads to deterioration of coercivity, especially for the high surface to volume ratio. Opposite effects were observed for soft magnetic fractals when the nanostructure caused an appearance of the coercive field, and the maximum of energy product was predictably significantly higher than for conventional rare earths’ free permanent magnets.

All‐Inorganic Nanocrystals as a Glue for BiSbTe Grains: Design of Interfaces in Mesostructured Thermoelectric Materials

AbstractNano‐ and mesostructuring is widely used in thermoelectric (TE) materials. It introduces numerous interfaces and grain boundaries that scatter phonons and decrease thermal conductivity. A new approach has been developed for the rational design of the interfaces in TE materials by using all‐inorganic nanocrystals (NCs) that serve as a “glue” for mesoscopic grains. For example, circa 10 nm Bi NCs capped with (N2H5)4Sb2Te7 chalcogenidometallate ligands can be used as an additive to BiSbTe particles. During heat treatment, NCs fill up the voids between particles and act as a “glue”, joining grains in hot‐pressed pellets or solution‐processed films. The chemical design of NC glue allowed the selective enhancement or decrease of the majority‐carrier concentration near the grain boundaries, and thus resulted in doped or de‐doped interfaces in granular TE material. Chemically engineered interfaces can be used as to optimize power factor and thermal conductivity.

All-inorganic nanocrystals as a glue for BiSbTe grains: design of interfaces in mesostructured thermoelectric materials.

Nano- and mesostructuring is widely used in thermoelectric (TE) materials. It introduces numerous interfaces and grain boundaries that scatter phonons and decrease thermal conductivity. A new approach has been developed for the rational design of the interfaces in TE materials by using all-inorganic nanocrystals (NCs) that serve as a "glue" for mesoscopic grains. For example, circa 10 nm Bi NCs capped with (N2H5)4Sb2Te7 chalcogenidometallate ligands can be used as an additive to BiSbTe particles. During heat treatment, NCs fill up the voids between particles and act as a "glue", joining grains in hot-pressed pellets or solution-processed films. The chemical design of NC glue allowed the selective enhancement or decrease of the majority-carrier concentration near the grain boundaries, and thus resulted in doped or de-doped interfaces in granular TE material. Chemically engineered interfaces can be used as to optimize power factor and thermal conductivity.

On the roles of Bi2Sr2CuOx intergrowths in Bi2Sr2CaCu2Ox/Ag round wires: c-axis transport and magnetic flux pinning

Despite progress in the performance of Bi2Sr2CaCu2Ox (Bi2212)/Ag multifilamentary round wires, understanding the impact of microstructural defects on multiple length scales on electrical transport remains a significant challenge. Many recent studies have focused on porosity, but porosity is not the only factor in determining Jc. The primary impurity in partial-melt processed multifilamentary Bi2212 wires is Bi2Sr2CuOx (Bi2201), which forms as mesoscopic grains and nanoscopic intergrowths. Previously, we showed the destructive effect of Bi2201 grains on transport. Here, we relate scanning transmission electron microscopy results to the Bi2212 coherence length, anisotropic magnetization behavior, and magnetic-field dependent transport to study c-axis transport and the effects of Bi2201 intergrowths on magnetic flux pinning. We show that wide Bi2201 intergrowths are barrier to c-axis transport within Bi2212 grains, whereas narrow (half- and full-cell) Bi2201 intergrowths are not detrimental to c-axis transport and are likely magnetic flux pinning centers. These results have significant impact on the understanding of Bi2212/Bi2201 systems and provide important physical insight towards future improvements in devices based upon wires, film, and junctions.

Stabilization of an ambient-pressure collapsed tetragonal phase in CaFe2As2and tuning of the orthorhombic-antiferromagnetic transition temperature by over 70 K via control of nanoscale precipitates

We have found a remarkably large response of the transition temperature of CaFe2As2 single crystals grown out of excess FeAs to annealing / quenching temperature. Whereas crystals that are annealed at 400 C exhibit a first order phase transition from a high temperature tetragonal to a low temperature orthorhombic and antiferromagnetic state near 170 K, crystals that have been quenched from 960 C exhibit a transition from a high temperature tetragonal phase to a low temperature, non-magnetic, collapsed tetragonal phase below 100 K. By use of temperature dependent electrical resistivity, magnetic susceptibility, X-ray diffraction, Mossbauer spectroscopy and nuclear magnetic resonance measurements we have been able to demonstrate that the transition temperature can be reduced in a monotonic fashion by varying the annealing / quenching temperature from 400 to 850 C with the low temperature state remaining antiferromagnetic for transition temperatures larger than 100 K and becoming collapsed tetragonal / non-magnetic for transition temperatures below 90 K. This suppression of the orthorhombic / antiferromagnetic phase transition and its ultimate replacement with the collapsed tetragonal / non-magnetic phase is similar to what has been observed for CaFe2As2 under hydrostatic pressure. Transmission electron microscopy studies indicate that there is a temperature dependent, width of formation of CaFe2As2 with a decreasing amount of excess Fe and As being soluble in the single crystal at lower annealing temperatures. For samples quenched from 960 C there is a fine (of order 10 nm), semi-uniform distribution of precipitate that can be associated with an average strain field whereas for samples annealed at 400 C the excess Fe and As form mesoscopic grains that induce little strain throughout the CaFe2As2 lattice.

Two-dimensional dusty plasma crystals and liquids

Strongly coupled plasmas - in which the average potential energy per particle dominates over the average kinetic energy - appear in a wide variety of physical systems. Among these systems, dust plasma crystals and liquids realized in low-pressure gas discharges by dispersing mesoscopic grains into the plasma have attracted a lot of attention during the past years. We describe the experimental realization of the quasi-two-dimensional dust system, summarize the basics of the computer simulation and theoretical approaches capable of their description in the liquid and solid phases. We discuss the properties of the dynamical density and current correlation spectra, generated by molecular dynamics simulations, and address the issues associated with the existence of different phases and transport coefficients (e.g. superdiffusive behavior) in the low-dimensional systems under study.

Superconductor-to-normal transitions in dissipative chains of mesoscopic grains and nanowires

The interplay of quantum fluctuations and dissipation in chains of mesoscopic superconducting grains is analyzed, and the results are also applied to nanowires. It is shown that in 1-d arrays of resistively shunted Josephson junctions, the superconducting-normal charge relaxation within the grains plays an important role. At zero temperature, two superconducting phases can exist, depending primarily on the strength of the dissipation. In the fully superconducting phase (FSC), each grain acts superconducting, and the coupling to the dissipative conduction is important. In the SC* phase, the dissipation is irrelevant at long wavelengths. The phase transitions between these two superconducting phases and the normal metallic phase may be either local or global, and possess rich and complex critical properties. These are inferred from both weak and strong coupling renormalization group analyses. At intermediate temperatures, near either superconductor-to-normal phase transition, there are regimes of super-metallic behavior, in which the resistivity first decreases gradually with decreasing temperature before eventually increasing as temperature is lowered further. The results on chains of Josephson junctions are extended to continuous superconducting nanowires and the subtle issue of whether these can exhibit an FSC phase is considered. Potential relevance to superconductor-metal transitions in other systems is also discussed.

Magnetic dipolar interaction in two-dimensional complex plasmas

Various interactions can play a role between the mesoscopic dust grains of a complex plasma. We study a system composed of dust grains that have both an electric charge and a permanent magnetic dipole moment. It is assumed that the grains occupy lattice sites, as dictated by their Coulomb interaction. In addition, they possess a spin degree of freedom (orientation of magnetic dipole moment) that is not constrained by the Coulomb interaction, thus allowing for the possibility of equilibrium orientational ordering and 'wobbling' about the equilibrium orientations. As a result, collective modes develop. We identify in-plane and out-of-plane wobbling modes and discuss their dispersion characteristics both in the ferromagnetic and in the anti-ferromagnetic ground state.

LargeNPenner matrix model and a novel asymptotic formula for the generalized Laguerre polynomials

The Gaussian Penner matrix model is re-examined in the light of the results which have been found in double-well matrix models. The orthogonal polynomials for the Gaussian Penner model are shown to be the generalized Laguerre polynomials L(α)n(x) with α and x depending on N, the size of the matrix. An asymptotic formula for the orthogonal polynomials is derived following closely the orthogonal polynomial method of Deo (1997 Nucl. Phys. B 504 609). The universality found in the double-well matrix model is extended to include non-polynomial potentials. An asymptotic formula is also found for the Laguerre polynomial using the saddle-point method by rescaling α and x with N. Combining these results a novel asymptotic formula is found for the generalized Laguerre polynomials (different from that given in Szego's book) in a different asymptotic regime. This may have applications in mathematical and physical problems in the future. The density–density correlators are derived and are the same as those found for the double-well matrix models. These correlators in the smoothed large N limit are sensitive to odd and even N where N is the size of the matrix. These results for the two-point density–density correlation function may be useful in finding eigenvalue effects in experiments in mesoscopic systems or small metallic grains. There may be applications to string theory as well as the tunnelling of an eigenvalue from one valley to the other being an important quantity there.

Mesoscopic magnetization fluctuations for metallic grains close to the Stoner instability

This paper is devoted to the magnetic properties of isolated mesoscopic grains. We demonstrate that under very general conditions the electron-electron interactions in such grains can be taken into account by a simple interaction Hamiltonian. This Hamiltonian involves only three coupling constants, which correspond to charging, exchange interaction, and superconducting correlations. The most important condition for such a description is that Thouless conductance of each grain is large. Under this condition sample-to-sample fluctuations of the coupling constants can be neglected. However, the thermodynamic properties can still remain sample specific due to the one-electron part of the Hamiltonian. If the grain is made from a material that is close to the threshold of ferromagnetic instability, the mesoscopic fluctuations of the magnetization are especially strong. Moreover, the situation becomes multistable: free energy of each grain as a function of the magnetization is characterized by a large number of local minima. We analyze the statistics of these minima and show that it possesses simple scaling properties. Numerical simulations confirm this scaling.

Investigation of an array of mesoscopic grains in the framework of quantum cosine model

An array of small superconducting grains on a conducting substrate is studied in the mean-field approximation and by mapping the system onto the classical XY-model. The quantum cosine model used does not contain an incorrect phase operator. A comparison with the results of quantum numerical modeling is performed.

Charge glass transition in disordered two-dimensional arrays of mesoscopic grains

Monte Carlo dynamics simulations of capacitively coupled conductors model with random offset charge disorders are performed in the infinite screening length limit to study the current–voltage ( I– V) characteristics in disordered two-dimensional arrays of mesoscopic grains coupled by tunneling. It is found that the linear conductance of the system at small bias voltages obeys the Arrenius dependence on temperature, in which the effective Coulomb barrier is reduced due to the charge fluctuation. With increasing the bias voltage the I– V curves are shown to cross over to the nonlinear behaviour, characterized by scaling properties. Such scaling properties are associated with a phase transition, which is named the charge glass transition from an analogy of the vortex glass transition in disordered superconducting films.

Order parameter quantum fluctuations in a two-dimensional system of mesoscopic Josephson junctions

The boson lattice Hubbard model is used to study the role of quantum fluctuations of the phase and local density of the superfluid component in establishing a global superconducting state for a system of mesoscopic Josephson junctions or grains. The quantum Monte Carlo method is used to calculate the density of the superfluid component and fluctuations in the number of particles at sites of the two-dimensional lattice for various average site occupation numbers n0 (i.e., number of Cooper pairs per grain). For a system of strongly interacting bosons, the phase boundary of the ordered superconducting state lies above the corresponding boundary for its quasiclassical limit—the quantum XY-model—and approaches the latter as n0 increases. When the boson interaction is weak in the boson Hubbard model (i.e., the quantum fluctuations of the phase are small), the relative fluctuations of the order parameter modulus are significant when n0<10, while quantum fluctuations in the phase are significant when n0<8; this determines the region of mesoscopic behavior of the system. Comparison of the results of numerical modeling with theoretical calculations show that mean-field theory yields a qualitatively correct estimate of the difference between the phase diagrams of the quantum XY-model and the Hubbard model. For a quantitative estimate of this difference the free energy and thermodynamic averages of the Hubbard model are expanded in powers of 1/n0 using the method of functional integration.

Mm-wave absorption by two level systems in mesoscopic amorphous grains

Abstract Temperature dependent mm-wave (0.7–3 mm) absorption in mesoscopic amorphous silicate grains synthesized by sol-gel reaction has been measured between 1.2 and 15 K. These amorphous powders are precursors to forsterite (Mg 2 SiO 4 ), enstatite (MgSiO 3 ) and MgO · 2SiO 2 . The measured bleaching of the absorption with increasing temperature characteristic of two level system behavior is observed in all cases and the results are compared with those obtained from bulk aerogel and soda-lime-silica glass. The weighted spectral density of two level states throughout this wavelength region is shown to be larger for all the silicate particles when compared with bulk soda-lime-silica glass.

Strong electron tunneling in mesoscopic metallic grains

Electron tunneling through mesoscopic metallic grains can be treated perturbatively only provided the tunnel junction conductances are sufficiently small. If it is not the case, fluctuations of the grain charge become strong. As a result (i) contributions of all—including high energy—charge states become important and (ii) excited charge states become broadened and essentially overlap. At the same time the grain charge remains discrete and the system conductancee-periodically depends on the gate charge. We develop a nonperturbative approach which accounts for all these features and calculate the temperature dependent conductance of the system in the strong tunneling regime at different values of the gate charge.

Quantum Tunneling of Magnetization in Nanostructured Materials

The study of very low temperature magnetic relaxation in nanostructured materials has provided the opportunity to observe the occurrence of quantum tunneling of magnetization (QTM) in many different systems. As the magnetization is a classical vector, this effect is also referred to as macroscopic quantum tunneling (MQT). In this paper, we review the key ideas underlying magnetic relaxation as well as the results obtained for different nanostructured systems, which, to date, include single domain particles, mesoscopic grains, and high-spin polynuclear molecules.

Isotopic-spin formulation of the Josephson effect.

A model for a quantum-mechanical weak link between two superconductors is discussed in which the tunneling of electron pairs is described by ``isotopic spin'' operators (${\mathit{T}}_{1}$,${\mathit{T}}_{2}$,${\mathit{T}}_{3}$) obeying [${\mathit{T}}_{\mathit{a}}$,${\mathit{T}}_{\mathit{b}}$]=i${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}\mathit{b}\mathit{c}}$${\mathit{T}}_{\mathit{c}}$. In the thermodynamic limit of infinite size for the superconductors, the model reduces to the quantum ``Josephson pendulum.'' However, the model also holds true for mesoscopic grains, and thus allows for the quantum description of lowest-order finite-size effects.