The Coriolis attenuation in the pairing plus recoil model

The attenuation factor of the Coriolis off diagonal matrix element has been found to be very sensitive to the pairing strength. About 10% extra reduction of the attenuation factor coming from the recoil term may be expected in the pairing plus recoil model for some Coriolis matrix elements, if a reasonable pairing gap parameter is taken.     

NUCLEAR PAIRING PHASE TRANSITION

The intrinsic structure of the eigenfunctions of Cranking Shell Model hamiltonian and the pairing phase transition at high rotational frequency are investigated with the particle-number-conserving approach.Pair-transfer matrix elements and the K-structure of the wave functions display similar behaviour under the Coriolis interaction and hence both of them may be used to indicate the pairing phase transition.The blocking effects on pairing parameter,,are much more important than the Coriolis anti-pairing effects.     

Pairing symmetries in cuprates: A Gorkov formalism

Inspite of the direct evidence for Cooper pairing in the cuprates as in conventional superconductors, the pairing symmetry in the cuprate superconductors is still considered to be a controversial and a highly debatable topic. The microscopic equations appropriate for these new materials, essentially the yttrium based compounds, are discussed following Gorkov's formalism for the conventional superconductors. Various types of symmetry of the pairing parameter are considered. In this study we consider the anisotropic nature of the gap parameter to write the mean-field equations of the cuprates. We observe that the symmetry of the potential is fundamental in deciding the nature of the anisotropy in the gap parameter.     

Effect of electron correlation on superconducting pairing symmetry

The role of electron correlation on different pairing symmetries are discussed in details where the electron correlation has been treated within the slave boson formalism. It is shown that for a pure s or pure d wave pairing symmetry, the electronic correlation suppresses the s wave gap magnitude (as well as the ) at a faster rate than that for the d wave gap. On the other hand, a complex order parameter of the form () shows anomalous temperature dependence. For example, if the temperature () at which the d wave component of the complex order parameter vanishes happens to be larger than that for the s wave component (), then the growth of the d wave component is arrested with the onset of the s wave component of the order parameter. In this mixed phase however, we find that the suppression in different components of the gap as well as the corresponding due to coulomb correlation are very sensitive to the relative pairing strengths of s and d channels as well as the underlying lattice. Interestingly enough, in such a scenario (for a case of )the gap magnitude of the d wave component increases with electron correlation but not for certain values of electron correlation. However, this never happens in case of the s wave component. We also calculate the temperature dependence of the superconducting gap along both the high symmetry directions ( and ) in a mixed symmetry pairing state and the thermal variation of the gap anisotropy [0pt][0pt] with electron correlation. The results are discussed with reference to experimental observations. Received: 26 August 1997 / Revised: 31 December 1997 / Accepted: 28 January 1998     

Pairing properties of nuclear matter at finite temperature

The Gogny effective interaction is used to calculate the pairing properties of symmetric nuclear matter at various densities and temperatures. A pairing collapse is predicted at a critical temperature of half the gap parameter at temperature zero. The phase diagram which separates normal and superfluid phases is calculated.     

Dynamical vanishing of the order parameter in a fermionic condensate

We analyze the dynamics of a condensate of ultracold atomic fermions following an abrupt change of the pairing strength. At long times, the system goes to a nonstationary steady state, which we determine exactly. The superfluid order parameter asymptotes to a constant value. We show that the order parameter vanishes when the pairing strength is decreased below a certain critical value. In this case, the steady state of the system combines properties of normal and superfluid states -- the gap and the condensate fraction vanish, while the superfluid density is nonzero.     

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.     

On limits of ab initio calculations of pairing gap in nuclei

A brief review of recent microscopic calculations of nuclear pairing gap is given. A semi-microscopic model is suggested in which the ab initio effective pairing interaction is supplemented with a small phenomenological addendum. It involves a parameter which is universal for all medium and heavy nuclei. Calculations for several isotopic and isotonic chains of semi-magic nuclei confirm the relevance of the model.     

Eliashberg Equations and Coulomb Pseudopotential for Superconductivity via Sign-Opposite Interactions

A new type of attractive interactions, the second retarded ones, is investigated with the Eliaehberg treatment. Several mechanisms, leading to the pairing in the high frequency window, belong to this type. The equations for gap parameter are derived. From these a formula of the Coulomb pseudopotential is obtained. It is found that the Coulomb repulsion against the pairing is completely suppressed by the pseudopotential effect in the unscreened case. Its significance for the high T_c superconductivity is discussed.     

Thermal and quantum fluctuations induced additional gap in single-particle spectrum of d-p model

The possibility of thermal and quantum fluctuations induced attractive interaction leading to a pairing gap Δ_tq in the single-particle spectrum of d-p model in the limit of a large N of fermion flavor is investigated analytically. This is an anomalous pairing gap in addition to the one with d-wave symmetry originating from partially screened, inter-site coulomb interaction. The motivation was to search for a hierarchy of multiple many-body interaction scales in high-T_c superconductor as suggested by recent experimental findings. The pairing gap anisotropy stems from more than one source, namely, nearest neighbor hoppings and the p-d hybridization, but not the coupling of the effective interaction. The temperature at which Δ_tq vanishes may be driven to zero by using a tuning parameter to have access to quantum criticality (QC) only when N?1. For the physical case N=2, the usual coherent quasi-particle feature surfaces in the spectral weight everywhere in the momentum below the pairing gap Δ_tq. Thus it appears that the reduction in spin degeneracy has the effect of masking quantum criticality.     

Temperature and magnetic field dependence of superconductivity in nanoscopic metallic grains

We study pairing correlations in ultrasmall superconductor in the nanoscopic limit by means of a toy model where electrons are confined in a single, multiply degenerate energy level. We solve the model exactly to investigate the temperature and magnetic field dependence of number parity effect (dependence of ground state energy on evenness or oddness of the number of electrons). We find a different parity effect parameter to critical temperature ratio (4 rather than 3.5) which turns out to be consistent with exact solution of the BCS gap equation for our model. This suggests the equivalence between the parity effect parameter and the superconducting gap. We also find that magnetic field is suppressed as temperature increases.     

Conductivity of superconducting chalcogenides

A theoretical study of a superconducting transition in many valley semiconductors, allowing interband electron-electron pairing, is presented. The order parameter, at very low temperatures, and the ac-conductivity are calculated and shown to reproduce known results in the limit when the “dielectric gap” is going to zero.     

The behavior of the temperature-dependent cranking mass parameter

The temperature dependence of the mass parameter is analyzed starting from the Inglis cranking formula. At temperatures higher than the critical temperature corresponding to a vanishing pairing gap, the mass parameter is found to approach that of the incompressible liquid drop value, at least qualitatively. This general result is tested for several simple cases where we can get almost analytical results. In these cases clear relations between the cranking mass and the incompressible liquid drop value are obtained.     

Phenomenological theory of the s-wave state in superconductors without an inversion center

In materials without an inversion center of symmetry the spin degeneracy of the conducting band is lifted by an antisymmetric spin orbit coupling (ASOC). Under such circumstances, spin and parity cannot be separately used to classify the Cooper pairing states. Consequently, the superconducting order parameter is generally a mixture of spin singlet and triplet pairing states. In this paper we investigate the structure of the order parameter and its response to disorder for the most symmetric pairing state (A₁). Using the example of the heavy Fermion superconductor CePt₃Si, we determine characteristic properties of the superconducting instability. Depending on the type of the pairing interaction, the gap function is characterized by the presence of line nodes. We show that this line nodes move in general upon temperature. Such nodes would be essential to explain recent low-temperature data of thermodynamic quantities such as the NMR-T₁ ^-1, London penetration depth, and heat conductance. Moreover, we study the effect of (non-magnetic) impurity on the superconducting state.     

Specific heat in superconductors

Specific heat is a powerful tool to investigate the physical properties of condensed materials. Superconducting state is achieved through the condensation of paired electrons, namely, the Cooper pairs. The condensed Cooper pairs have lower entropy compared with that of electrons in normal metal, thus specific heat is very useful in detecting the low lying quasiparticle excitations of the superconducting condensate and the pairing symmetry of the superconducting gap. In this brief overview, we will give an introduction to the specific heat investigation of the physical properties of superconductors.We show the data obtained in cuprate and iron based superconductors to reveal the pairing symmetry of the order parameter.     

Layered superconductors with anisotropic energy gap: specific heat and infrared absorption

New oxide superconductors with layered structure are expected to have anisotropic energy gap in the generalized BCS pairing theory. The gap parameter can be quite different for perpendicular to the plane of the layers as compared tok parallel to layer planes. Because of short coherence lengths ξ, quite small compared to the normal state carrier meanfree pathl, the effect of these anisotropies do not average out, as in many of the conventional superconductors. For a proper comparison of experimental results with the correct predictions of the pairing theory, a formulation is developed to obtain important physical quantities like specific heat and infrared absorption in the superconducting state of such anisotropic systems. This includes a brief account of the pairing theory generalized to layered crystals with arbitrary number of layers per unit cell, not necessarily equidistant. In an explicit model for the anisotropy of the gap parameter ink-space, with a simple form for the nonspherical Fermi-surface, it is shown that the low-temperature specific heat can have even a linear or a power-law temperature-dependence in the superconducting state. Even if the gap parameter does not vanish anywhere, its smeared-out exponential temperature-dependence may be difficult to be distinguished experimentally from a power-law behaviour. Similarly, it is shown that in the case of appreciable anisotropy, infrared absorption can take place much below the in-plane gap parameter , wherek _t is the wavevector in the plane of the layers.     

Andreev states near short-ranged pairing potential impurities

We study Andreev states near atomic scale modulations in the pairing potential in both s- and d-wave superconductors with short coherence lengths. For a moderate reduction of the local gap, the states exist only close to the gap edge. If one allows for local sign changes of the order parameter, however, resonances can occur at energies close to the Fermi level. The local density of states (LDOS) around such pairing potential defects strongly resembles the patterns observed by tunneling measurements around Zn impurities in Bi2Sr2CaCu2O8+x (BSCCO). We discuss how this phase impurity model of the Zn LDOS pattern can be distinguished from other proposals experimentally.     

Superfluid pairing gap in strong coupling

The zero-temperature pairing gap is a fundamental property of interacting Fermions, providing a crucial test of many-body theories in strong coupling. We analyze recent cold-atom experiments on imbalanced Fermi systems using Quantum Monte Carlo results for the superfluid and normal phases. Through this analysis we extract, for the first time, the experimental zero-temperature pairing gap in the fully paired superfluid state at unitarity where the two-body scattering length is infinite. We find that the zero-temperature pairing gap is greater than 0.4 times the Fermi energy E(F), with a preferred value of (0.45+/-0.05) E(F). The ratio of the pairing gap to the Fermi Energy is larger here than in any other Fermi system measured to date.     

基于相对论平均场有效对力的中子物质BCS-BEC渡越

基于核物质的相对论Hartree-Bogoliubov（RHB）理论,采用相对论平均场单玻色子交换形式的有效对相互作用,研究了不同对力强度下双中子关联及其中的BCS-BEC渡越现象。通过引入有效衰减因子χ调节对力强度,定量分析费米面处中子对能隙和单粒子动能比值△_Fn/e_Fn及无量纲参数1/（k_Fna）随费米动量k_Fn的演化行为,发现双中子对在χ=0.51时进入BCS-BEC渡越区域,在χ=0.67时可达到幺正极限。进而分析了中子对能隙、中子对波函数及相干长度等物理量在相应临界点处的特征,并给出渡越时双中子短程关联概率的定量判据。发现当配对中子处于平均中子间距以内的概率P（d_n）?0.80时,双中子对从纯BCS耦合过渡到BCS-BEC渡越区域。Based on the relativistic Hartree-Bogoliubov theory in nuclear matter, the dineutron correlations and the crossover from Bardeen-Cooper-Schrieffer (BCS) region of neutron Cooper pairs to Bose-Einstein condensation (BEC) are investigated with the one-boson-exchange type of pairing force generated from the relativistic mean field (RMF) model. By introducing an effective factor χ in the RMF effective pairing interaction, the density dependence of the ratios between neutron pairing gap at Fermi surface and neutron Fermi kinetic energy △_Fn/e_Fn and the dimensionless parameter 1/(k_Fna) are analyzed quantitatively. Then the criteria where dineutron correlations exactly reach the threshold of BCS-BEC crossover or unitary limit are determined to be χ=0.51 or 0.67, respectively. In addition, features of neutron pairing gap, Cooper pair wave function and dineutron coherence length are illustrated, and the value of the probability for partner neutrons correlated within the average inter-neutron distance, namely P (d_n) ?0.80, is obtained as a criterion of BCS-BEC crossover.     

New gap equation for strongly correlated metals

Assuming a phenomenological self-energy ImΣ(ω)|ω|^β, (β=1), which becomes gapped below T_c, we derived a new gap equation. The new gap equation contains the effect of the kinetic energy gain upon developing a superconducting order parameter. However, this new kinetic energy gain mechanism works only for a repulsive pairing potential leading to a s-wave state. In this case, compared to the usual potential energy gain in the superconducting state as in the BCS gap equation, the kinetic energy gain is more effective to easily achieve a high critical temperature T_c, since it is naturally Fermi energy scale. In view of the experimental evidences of a d-wave pairing state in the hole-doped copper-oxide high-T_c superconductors, we discuss the implications of our results.