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 origin of the pseudogap phase: precursor superconductivity versus a competing energy gap scenario

In the last few years evidence has been accumulating that there are a multiplicity of energy scales which characterize superconductivity in the underdoped cuprates. In contrast to the situation in BCS superconductors, the phase coherence temperature T_c is different from the energy gap onset temperature T^∗. In addition, thermodynamic and tunneling spectroscopies have led to the inference that the order parameter Δ_sc is to be distinguished from the excitation gap Δ; in this way, pseudogap effects persist below T_c. It has been argued by many in the community that the presence of these distinct energy scales demonstrates that the pseudogap is unrelated to superconductivity. In this paper, we show that this inference is incorrect. We demonstrate that the difference between the order parameter and excitation gap and the contrasting dependences of T^∗ and T_c on hole concentration x and magnetic field H follow from a natural generalization of BCS theory. This simple generalized form is based on a BCS-like ground state, but with self-consistently determined chemical potential in the presence of arbitrary attractive coupling g. We have applied this mean field theory with some success to tunneling, transport, thermodynamics, and magnetic field effects. We contrast the present approach with the phase fluctuation scenario and discuss key features which might distinguish our precursor superconductivity picture from that involving a competing order parameter.     

Debye等离子体中高能H++H碰撞激发过程的研究

利用碰撞参数玻恩近似方法研究了Debye 等离子体环境中高能H⁺+H的碰撞激发过程, 研究了不同Debye 半径下氢原子1s → 2p 的激发耦合相互作用矩阵元、入射粒子能量为160 keV/u 的激发电子跃迁概率以及入射粒子能量范围为100–1000 keV/u 的碰撞激发截面. 结果表明: 随着屏蔽效应的增强, 激发截面减小. 根据激发截面的公式以及计算结果详细分析了引起激发截面减少的原因. 入射粒子与激发电子之间的屏蔽相互作用势和靶的电子结构(波函数和能级) 对激发截面都有很重要的影响. 关键词： 等离子体 碰撞参数玻恩近似方法 碰撞激发截面     

Shell effects in a paired nucleus for finite excitation energies

Shell effects are considered as functions of the excitation energy of the nucleus. The effects of pairing are included and studied in the BCS approximation. Some numerical results, based on the single-particle spectrum of a Woods-Saxon potential, are given. In the limit of zero excitation the shell correction to the energy is compared with the results obtained by the Strutinsky method.     

Influence of particle number fluctuations and vibrational modes on thermodynamic characteristics of a hot nucleus

Nogami's method is extended to finite temperatureT. The effect of quantum and statistical fluctuations for the particle number in the finite temperature BCS model on the excitation energy, entropy, specific heat, level density and level density parameter is calculated in hot⁵⁸Ni nucleus. The calculations have been performed with the finite temperature BCS gap and statistical average gap due to the finiteness of nucleus. In the finite temperature RPA the contribution of dipole and quadrupole vibrational modes to the specific heat and the increase of level density is calculated.     

Gap inhomogeneities and the density of states in disordered d-wave superconductors

We report on a numerical study of disorder effects in 2D d-wave BCS superconductors. We compare exact numerical solutions of the Bogoliubov-de Gennes (BdG) equations for the density of states rho(E) with the standard T-matrix approximation. Local suppression of the order parameter near impurity sites, which occurs in self-consistent solutions of the BdG equations, leads to apparent power-law behavior rho(E) approximately |E|(alpha) with nonuniversal alpha over an energy scale comparable to the single-impurity resonance energy Omega(0). We show that the novel effects arise from static spatial correlations between the order parameter and the impurity distribution.     

Josephson effect between superconducting nanograins with discrete energy levels

We investigate the Josephson effect between two coupled superconductors, coupled by the tunneling of pairs of electrons, in the regime that their energy level spacing is comparable to the bulk superconducting gap, but neglecting any charging effects. In this regime, BCS theory is not valid, and the notion of a superconducting order parameter with a well-defined phase is inapplicable. Using the density matrix renormalization group, we calculate the ground state of the two coupled superconductors and extract the Josephson energy. The Josephson energy is found to display a reentrant behavior (decrease followed by increase) as a function of increasing level spacing. For weak Josephson coupling, a tight-binding approximation is introduced, which illustrates the physical mechanism underlying this reentrance in a transparent way. The DMRG method is also applied to two strongly coupled superconductors and allows a detailed examination of the limits of validity of the tight-binding model.Received: 8 September 2003, Published online: 28 May 2004PACS: 74.20.-z Theories and models of superconducting state - 74.78.-w Superconducting films and low-dimensional structures - 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects     

Studies on the vibrational excitation differential cross sections of non-resonant e-N2 scattering using augmented polarization potentials

Distributed spherical Gaussian (DSG) correlation-polarization model potentials with higher-order terms and exact exchange effects in single-configuration Slater determinant are taken into account for low-energy vibrational excitation e-N₂ scattering system. The integrodifferential coupled channel equations are solved using a combination of linear-algebraic and R-matrix-propagator algorithms. Analytic Born completion is used to calculate high-order scattering matrix elements in order to obtain convergent differential cross sections. The energy range is set to 4–15 eV which is not tested by the present theoretical method before. The overall agreement of theoretical results with the latest experiments emphasizes the importance of higher-order correlation-polarization potentials and rigorous exchange effects in vibrational excitation scattering.     

Study of the muon number violating (μ, e conversion in a nucleus by using quasi-particle RPA

The exotic (μ⁻, e⁻) conversion reaction for the ⁴⁸Ti nucleus is studied in the framework of the quasi-particle random phase approximation (QRPA). For the non-coherent processes the relevant total rate is calculated by summing over partial rates for all the possible intermediate states constructed in the above approximation. For the coherent process the contribution is obtained by using an uncorrelated BCS vacuum. In order to check the validity of closure approximation, which is almost unavoidable in shell-model calculations, we also evaluate the total (μ⁻, e⁻) conversion rates by QRPA sum-rules by first explicitly calculating a suitable mean excitation energy of the nucleus. The influence of the ground state correlations to the (μ⁻, e⁻) conversion matrix elements is estimated by using a correlated RPA vacuum. The fraction of the transition rate of the coherent process for each of these methods is calculated and the results are compared to those found previously by using shell-model closure approximation.     

Pairing in 4-component fermion systems: The bulk limit of SU(4)-symmetric Hamiltonians

Fermion systems with more than two components can exhibit pairing condensates of a much more complex structure than the well-known single BCS condensate of spin-up and spin-down fermions. In the framework of the exactly solvable SO(8) Richardson-Gaudin (RG) model with SU(4)-symmetric Hamiltonians, we show that the BCS approximation remains valid in the thermodynamic limit of large systems for describing the ground-state energy and the canonical and quasiparticle excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of collective excitations, but these do not affect the bulk energy and quasiparticle gaps.     

Superconductivity of small metal grains

1 IntroductionThe superconductivity of small metallic grains has been attracting a lot of attentions. On one hand, Anderson[1] predicted that the superconductivity would disappear if a me- tallic grain was so small that the spaces between the nearest neighbor energy levels in the system became larger than the energy gap of the bulk metallic superconductor; On the other hand, it was found in experiments made in the 1960s[2] that the critical tem- perature of superconductivity of small metallic …     

Multi-band pairing of ultrarelativistic electrons and holes in graphene bilayer

Multi-band pairing of effectively ultrarelativistic electrons and holes in asymmetrically biased graphene bilayer in strong coupling regime is considered. In this regime, the pairing affects both conduction and valence bands of the both graphene layers, and the order parameter is a matrix, which indices correspond to the bands. For band-diagonal s-wave pairing, we derive the system of multi-band gap equations for the gaps in the valence and conduction bands and solve it in the approximation of constant gaps and in the approximation of separable pairing potential. For a characteristic width of the pairing region of order of magnitude of the chemical potential, the gap values are not much different from single-band BCS estimations. However, if the pairing region is wider, then the gaps can be much larger and depend exponentially on its energy width. We also predict gapped and soliton-like oscillations of a relative phase of the gaps and unpairing of quarter-vortices at Kosterlitz-Thouless transition.     

DC and AC Josephson effects with superfluid Fermi atoms across a Feshbach resonance

We show that both DC and AC Josephson effects with superfluid Fermi atoms in the BCS-BEC crossover can be described at zero temperature by a nonlinear Schrodinger equation (NLSE). By comparing our NLSE with mean-field extended BCS calculations, we find that the NLSE is reliable in the AAN side of the crossover up to the unitarity limit. The NLSE can be used for weakly-linked atomic superfluids also in the BCS side of the crossover by taking the tunneling energy as a phenomenological parameter.     

Influence of the charge concentration on the density of states in a two-dimensional superconducting system

The gap and the density of states of high-T_c superconductors have been a subject of paramount interest. In order to explain the observed experimental behavior several pairing mechanisms in high-temperature superconductivity have been considered, by theoretical calculations. In this work, within the BCS scheme, a two-band model with energy band overlapping is introduced. The gap parameter and the density of states in a two-dimensional superconducting system are studied as functions of the charge concentration. This model is applied to Bi2212 in order to obtain numerical results.     

First Principle Calculations of Quasiparticle Energies for Band Structures of Semiconductors

We successfully applied the Green function theory in GW approximation to calculate the quasiparticle energies for semiconductors Si and GaAs. Ab initio pseudopotential method was adopted to generate basis wavefunctions and charge densities for calculating dielectric matrix elements and electron self-energies. To evaluate dynamical effects of screened interaction, GPP model was utilized to'extend dieletric matrix elements from static results to finite frequencies. We give a full account of the theoretical background and the technical details for the first principle pseudopotential calculations of quasiparticle energies in semiconductors and insulators. Careful analyses are given for the effective and accurate evaluations of dielectric matrix elements and quasiparticle self-energies by using the symmetry properties of basis wavefunctions and eigenenergies. Good agreements between the calculated excitation energies and fundamental energy gaps and the experimental band structures were achieved.     

Microscopic transport theory of heavy-ion collisions

Drift and diffusion coefficients for the variables of mass fragmentation and excitation energy are studied for deeply inelastic collisions. The transport coefficients are obtained in closed form as functions of the parameters of the interaction matrix elements between nucleonic states and as functions of the binding energy of the intermediate rotating quasimolecular configuration. Drift and diffusion coefficients for excitation and mass transfer are related (dissipation fluctuation theorem). In good approximation these relations take the simple form of Einstein's relation between the mobility and the diffusion coefficient of a particle in a medium. For the total mass numbers 100, 250 and 500 the results are discussed in detail. The transport coefficients are compared with experimental results. Within the uncertainties of determination from experimental data, the drift and diffusion coefficients are well described by two previously adjusted parameters of the mean interaction matrix elements. Consequences for the production of superheavy elements in deeply inelastic collisions of U on U or Cf are discussed.     

On the relaxation of the order parameter in the BCS model

The relaxation of the nonequilibrium order parameter (wave function of pairs) of a “pure” superconductor is considered for the homogeneous case. The relaxation is due to the electron-phonon interaction. The orderparameter relaxation time is shown to be much longer than the time interval between electron-electron collisions. This relation is explained by the smallness of the superconducting transition temperature compared to both the Fermi energy and the Debye energy in the BCS model.     

THE MICROSCOPIC CALCULATION OF THE STATISTICAL THEORY OF NUCLEAR FISSION

Based on the statistical fission theory, we have calculated the mass and kinetic energy distributions as well as other physical quantities of ²³⁵U fission induced by thermal neutron using microscopical method. That is, the quantum state densities of the fragments at scission point are calculated by means of BCS hamiltonian. The contribution of the collective deformation of fragments to the quantum state density has been taken into consideration. The potential energy of fragment is calculated by means of Strutinski procedure, and the shelling effect, pairing correlation as well as collective deformation have been taken into consideration in calculating the excitation energy at scission point. The scission point distance is treated as an adjustable parameter.Comparing with other statistical fission theories, our results give better agreement with existing experiments.     

浅海声场单模闭环发射的最佳估计算法

提出了一种浅海声场单模闭环发射的最佳估计算法。通过对声场格林函数矩阵估计协方差的分析,设计了一种对格林函数矩阵作最佳估计的最佳发射阵权系数矩阵,此权系数矩阵为酉矩阵且各元素绝对值相等。基于此矩阵的单模发射算法可以使得单模激发过程以最快的速度收敛,并且发射稳定。算法的优势在模拟计算中得到了验证。最后给出了海上实验的结果,单模含量高达97%。