LEVEL STATISTICS AND PARITY EFFECT ON SMALL SUPERCONDUCTING SYSTEMS

In this paper we have calculated the variations of the gap Δ'(0,d) and transition temperature T'_c in small metallic grains as functions of grain size (or the level spacing d between discrete electronic states) for the cases of odd and even numbers of electrons by applying the random matrix theory to the mean field theory. We find the presence of enhancement of superconductivity and critical d_c, where the superconductivity of small grains breaks down. This agrees with Anderson's prediction (1959 J. Phys. Chem. Solids 11 28). We find that in the grains, as the size is lowered, the transition temperature T'_c decreases and Δ'(0,d)/k_BT'_c≤πe_-γ in odd numbers of electrons, and for Gaussian orthogonal and unitary ensembles in some regimes Δ'(0,d)/k_B T'_c>πe_-γ in even numbers of electrons.     

Superconductivity in ultrasmall metallic grains

We review recent experimental and theoretical work on superconductivity in ultrasmall metallic grains, i.e. grains sufficiently small that the conduction electron energy spectrum becomes discrete. The discrete excitation spectrum of an individual grain can be measured by the technique of single‐electron tunneling spectroscopy, and reveals parity effects indicative of pairing correlations in the grain. After introducing the discrete BCS model that has been used to model such grains, we review a phenomenological, grand‐canonical, variational BCS theory describing the paramagnetic breakdown of these pairing correlations with increasing magnetic field. We also review recent canonical theories that have been developed to describe how pairing correlations change during the crossover, with decreasing grain size, from the bulk limit to the limit of few electrons, and compare their results to those obtained using Richardson's exact solution of the discrete BCS model.     

The energy spectral analysis of the strong-coupled superlattice

We study the energy spectrum of the strong-coupled superlattice. The barriers affect the energy spectral statistics in a small scale. The nearest-neighbor energy-level distribution P(s) and the spectral rigidity Δ₃(L) demonstrated the GOE (Gaussian Orthogonal Ensemble) distribution. In the whole scale, with the electric field increasing, the spectral rigidity Δ₃(L) changes from the Poisson-type like distribution to the Wigner-type like distribution due to the change of the energy-level long-correlation, while the P(s) indicates that the system demonstrates to be integrable. The near-degeneracy of levels makes the level statistics complex.     

Normal-state transport properties of Ba1−xKxBiO3 crystals

The normal-state transport properties of Ba_1−xK_xBiO₃ crystals with a wide range of potassium compositions (0≤x≤0.62) were studied. Although the host material BaBiO₃ has a monoclinic structure, the system changes from a monoclinic to an orthorhombic structure with a small doping of potassium (0≤x<0.35) and behaves similar to a doped semiconductor, without exhibiting superconductivity. In the composition range, holes are majority carriers in the transport phenomena. When x exceeds a critical value (0.35), the system goes into a cubic superconducting phase with a single metallic band. The vicinity of the critical composition transport phenomena is easy to understand assuming the existence of two conducting channels that are made up of metallic and semiconducting phases. Maximum T_c exceeding 30 K was observed at x0.4, where carrier density was at its maximum. Overdoping with potassium suppresses superconductivity. In the metallic composition of x>0.45, transport seems to correlate with the phonon mode with an energy distribution of 15–43 meV.     

HighT c superconductive materials: Bulk or twinned domain/grain boundary percolative network superconductors?

We have studied the physical properties of Y–Ba–Cu–Oxide superconducting materials by using Levitation, AC-susceptibility, macroscopic conductivity, Scanning Tunneling Microscopy (STM) local conductivity, Scanning Electron Microscope (SEM), X-rays, and Hall effect experimental techniques. Our results tend to indicate systematically that the grains formed in the synthesis do not show bulk superconductivity but rather are superconductors at the domain boundaries of the orthorhombic phase. It seems that a coexistence of semiconductor and metallic regions are formed at the twinned domain boundaries. The pellets become superconductors when the grains form clusters and are in intimate contact. This seems to suggest that the bulk of the grains is semiconducting and that a conducting percolative network of grain and domain boundaries may be responsible for the superconductivity. To understand the observed constant high transition temperature we propose a model of semiconductor-metal-semiconductor boundaries that give rise to superconductivity in a model like that of Little, Ginzburg, and Allender-Bray-Bardeen (1).     

Suppression of superconductivity in granular metals

We investigate the suppression of the superconducting transition temperature due to Coulomb repulsion in granular metallic systems at large tunneling conductance between the grains, g(T)>1. We find the correction to the superconducting transition temperature for 3D granular samples and films. We demonstrate that, depending on the parameters of superconducting grains, the corresponding granular samples can be divided into two groups: (i). the granular samples that belong to the first group may have only insulating or superconducting states at zero temperature depending on the bare intergranular tunneling conductance g(T), while (ii). the granular samples that belong to the second group in addition have an intermediate metallic phase where superconductivity is suppressed while the effects of the Coulomb blockade are not yet strong.     

两相钛合金再结晶退火组织与织构演变的蒙特卡罗模拟

蒙特卡罗(MC)方法被广泛应用于模拟金属材料在退火过程中的静态再结晶行为. 在已有两相材料晶粒长大MC模型基础上, 引入形核阶段, 综合考虑再结晶晶粒吞并形变晶粒和再结晶晶粒竞争长大两种情况, 建立了退火时两相合金再结晶MC模型.结合电子背散射衍射所测 初始晶粒形貌、相成分、晶体学取向及应变储能相对值, 该模型被应用于TC11钛合金退火过程中的微观组织及织构演变模拟.结果表明, 所建模型能够较好体现退火过程中两相晶粒的形核及晶粒长大行为. 与β相相比较, α相具有较低的再结晶速率和较高的晶粒长大速率, 前者主要归结于α相较低的初始应变储能, 后者则体现了该条件下初始组织形貌、分布及两相比例对晶粒长大具有重要影响; 由于非均匀形核的影响, 模拟得到的再结晶速率变化与 假设均匀形核的Johnson-Mehl-Avrami-Kolmogorov 再结晶方程存在明显差异.同时, 两相的基本织构特征在退火过程中无明显变化, 但织构强度增加. 关键词： 两相钛合金 再结晶 蒙特卡罗方法 织构     

Magnetization of small lead particles

The magnetization of an ensemble of isolated lead grains of sizes ranging from 4 to 1000 nm is measured. A sharp disappearance of the Meissner effect with a lowering of the grain size is observed for the smaller grains. This is a direct observation by magnetization measurement of the occurrence of a critical particle size for superconductivity, which is consistent with Anderson's criterion.     

Unraveling the symmetry of the hole states near the Fermi level in the MgB2 superconductor

We use x-ray absorption spectroscopy (XAS) and electron energy loss spectroscopy (EELS) to study the fine structure at the K edge of boron in MgB(2). We observe in XAS a peak of width 0.7 eV at the edge threshold, signaling a narrow energy region with empty boron p states near the Fermi level. The changes in the near edge structure observed in EELS with direction of the momentum transfer imply that these states have p(x)p(y) symmetry. Our observations are consistent with electronic structure calculations indicating a narrow energy window of empty p(x)p(y) states that falls to zero at 0.8 eV above the Fermi level. The disappearance of the p(x)p(y) feature in EELS at grain boundaries suggests that this signature may become powerful in probing superconductivity at nanoscale.     

Note on Mechanism for Formation of Bulbs (Structures) in Complex Plasmas with Grains of Different Size

In this note the phenomena of formation of grain bulbs (compact grain structure) in presence of grains with different size is discussed from point of view of grain force balance. The requirement is found showing where in the equilibrium conditions the larger size grains are expelled from the regions of smaller size grains forming dust bulbs containing only the smallest size grains. The experiments where this phenomenon was observed are discussed. It is possible to conclude that these experiments can serve as direct evidence for existence of the non‐linear screening of individual grains and for excitation of collective large scale electric fields that balances the drag forces in domain of structures. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A simple tight-binding approach to topological superconductivity in monolayer MoS_2

Monolayer molybdenum disulfide(MoS_2) has a honeycomb crystal structure.Here,with considering the triangular sublattice of molybdenum atoms,a simple tight-binding Hamiltonian is introduced(derived) for studying the phase transition and topological superconductivity in MoS_2 under uniaxial strain.It is shown that spin-singlet p+ip wave phase is a topological superconducting phase with nonzero Chern numbers.When the chemical potential is greater(smaller) than the spin-orbit coupling(SOC) strength,the Chern number is equal to four(two) and otherwise it is equal to zero.Also,the results show that,if the superconductivity energy gap is smaller than the SOC strength and the chemical potential is greater than the SOC strength,the zero energy Majorana states exist.Finally,we show that the topological superconducting phase is preserved under uniaxial strain.     

Ultra-small metallic grains: effect of statistical fluctuations of the chemical potential on superconducting correlations and vice versa

Superconducting correlations in an isolated metallic grain are governed by the interplay between two energy scales: the mean level spacing δ and the bulk pairing gap Δ0, which are strongly influenced by the position of the chemical potential with respect to the closest single-electron level. In turn superconducting correlations affect the position of the chemical potential. Within the parity projected BCS model we investigate the probability distribution of the chemical potential in a superconducting grain with randomly distributed single-electron levels. Taking into account statistical fluctuations of the chemical potential due to the pairing interaction, we find that such fluctuations have a significant impact on the critical level spacing δc at which the superconducting correlations cease: the critical ratio δc/Δ0 at which superconductivity disappears is found to be increased.     

Enhanced Intensity Fluctuations of Multiply Scattered Light in Nonlinear Absorbing Media

The properties of light transmission and interference phenomena in high dense media are investigated by means of numerical simulations in terms of nonlinear optical effect. Large intensity fluctuations are observed for nonlinear absorbing media, and do not agree with the fact that a decrease in absorption efficiency results in smaller intensity fluctuations for linear absorption media. From a variation in the speckle contrast it is found that the high-order path-crossing contributes to such intensity fluctuations. Moreover, the probability density of the total transmission changes from Gaussian statistics to log-normal ones for the small total transmission and to negative exponential ones for the large transmission, both of which appear in the strong localization regime. This indicates that the localization of optical waves might be controlled by the nonlinearity of the media.     

晶粒易轴取向度对纳米晶永磁Pr2Fe14B磁性的影响

构造了立方和不规则形状晶粒的各向异性纳米晶单相Pr₂Fe₁₄B磁体 .利用微磁学的有限元法，模拟计算了样品的磁滞回线.计算结果表明，随着磁体晶粒易轴取向度的变差， 磁体的剩磁、矫顽力均随之下降.不同晶粒尺寸的纳米晶单相Pr₂Fe_{14B磁体，其磁 性能随取向度的变化快慢不同，原因在于磁体中的晶间交换作用 (IGEC) 的强弱不同.随着 晶粒取向度的提高，纳米晶单相磁体的矫顽力逐渐增加，这完全不同于烧结磁体. 关键词： 纳米晶磁体 矫顽力 剩磁}     

Fabrication and Investigation of Photovoltaic Converters Based on Polycrystalline Silicon Grown on Borosilicate Glass

The microcrystalline Si layers with grain sizes of up to several tens of micrometers were grown. The physical vapor deposition (PVD), amorphous–liquid–crystalline (ALC) transition technique and a steady-state liquid phase epitaxy (SSLPE) are used for the fabrication of three different samples. The first sample under consideration was prepared first by deposition of a-Si onto glass substrates by PVD at room temperature, followed by heating from the front side to ~300°C and deposition of an indium metallic solvent. At the preparation of the second sample, an additional silicon layer with the thickness of 400 nm was deposited. A sample, when after that a c-Si was grown on the seed layer by SSLPE from indium solution is referred as a third sample. The resulting samples have a strong absorption edge in the mid-infrared region around 1960 cm^?1. Six well-resolved oscillations with an average period of δB = 0.1214 T are revealed on the third sample’s magnetoresistance curve at gradually increasing of the magnetic field from zero up to 1.6 T. It is assumed that either Aharonov–Bohm effect or kinetic phenomena taking place in the grains boundaries at lateral current flow are responsible for those oscillations. Quantitative evaluations show that due to the strong absorption in mid-infrared region, enlargement of the photoresponse spectrum will occur and the efficiency of solar and other thermal energy conversion should be around ~10–15% higher than that of traditional PV cells based on silicon on glass structures.     

The effect of shape and size on the electronic properties of ultrafine metallic particles

The subject of ultrafine metallic particles is treated with emphasis on energy level statistics. The energy level statistics so far proposed are reviewed based on the effect of shape of particles. The deviation of the nature of the chemical bond and that of magnetic properties in small size systems from those of bulk is described. The relevant electronic properties are expressed by formulae that incorporate the effect of shape in addition to size. New and old experiments including NMR Knight shift and static magnetic susceptibility are analyzed by means of the proposed formulae. The shape of particles is discussed in connection with the preparation methods. A concept of “the degree of metallicity” is introduced to characterize the statistics of level spacing fluctuation of small metal particles. A number of electronic properties of small size materials are also explained in terms of their sizes. The systems examined are small particles and conjugated chain compounds. The concept of zero-dimensionality is proposed and it is correlated with certain conservation laws such as topological invariance (conservation of shape) and as a conservation of the number of spins (parity of electrons).     

Surface modes in metal–insulator composites with strong interaction of metal particles

We theoretically examine plasmonic resonance excited between two close metallic grains embedded into a dielectric matrix. The grains sizes are assumed to be much less than the wavelength of the electromagnetic wave in the dielectric medium and the grain’s separation is assumed to be much smaller than the grains sizes. A qualitative scheme is developed that enables one to estimate frequency of the plasmonic resonance and value of the field enhancement inside the gap. Our general arguments are confirmed by rigorous analytic solution of the problem for simplest geometry—two identical spherical grains.     

The heat capacity of small metallic grains studied by the random matrices theory

The random matrices theory is applied to a study of the heat capacity of small metallic grains. The numerical calculations indicate that the level distribution and the difference between the particles respectively with an even and an odd numbers of electrons are important for the heat capacity of the small metallic grains at a low temperature and the level correlation mainly affects the heat capacity at a high temperature.     

The critical current of the superconductive tunnel junctions containing superconductive grains embedded in the oxide barrier

The superconductive tunnel junctions containing small superconductive grains embedded in the oxide barrier are investigated by the model of one dimensional atomic chains. The distribution of the Fermi levels of the grains relative to the Fermi level of the bulk superconductor is also taken into account. The results obtained indicate that the supercurrent appears only in the case that the charge energy of the grains is less than some certain value. The critical supercurrent of the junctions at zero temperature decreases as the charge energy of the grains increases. Temperature dependences of the critical supercurrents of junctions with different charge energies are also presented.