BCS Type Research Articles

Meissner effect of superconducting InN

AbstractWe report on the BCS‐type superconductivity of InN. A sample with a carrier concentration ne of 7×1018cm–3 is found to become zero resistance at ∼0.8 K and show BCS type Meissner effect at 0.2 K onset. Though the vortex solid is melted by thermal fluctuation and by external magnetic field from ∼2.5 K, the occurrence of the Meissner phase is suppressed by localized carriers along [10$ \bar 1 $0], which changes the character of the superconductivity into BCS type and the coherent length becomes comparable to that of ideal metal In. A mechanism which causes superconductivity in InN is proposed on the basis of the residual carriers produced by the interaction among the second nearest neighbor In‐In atoms originating from In 4d and N 2s hybridization (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Interplay of Phonon and Magnetic Mechanism of Pairing in Strongly Correlated Electron System of High-T c Cuprates

We consider magnetic mechanism of superconducting pairing in the effective low energy t−t′−t″−J* model with all parameters calculated ab initio. Interaction of strongly correlated electrons with different phonon modes is also incorporated. In a BCS type theory, the \(d_{x^{2}-y^{2}}\) gap is given by a sum of magnetic and phonon contributions. The main contribution to the only fitting parameter G is determined by a competition of the breathing and buckling modes. Fitting the parameter G from the isotope effect, we obtain that magnetic and phonon contributions to the critical temperature Tc work together and are of the same order of magnitude.

Theory of superconductivity for Dirac electrons in graphene

Phonon-exchange-induced superconducting pairing of effectively ultrarelativistic electrons in graphene is investigated. The Eliashberg equation obtained for describing pairing in the Cooper channel with allowance for delayed interaction are matrix equations with indices corresponding to the valence and conduction bands. The equations are solved in the high doping limit, in which pairing is effectively a single-band process, and in the vicinity of a critical quantum point of underdoped graphene for a value of the coupling constant for which pairing is an essentially multiband process. For such cases, analytic estimates are obtained for the superconducting transition temperature of the system. It is shown that the inclusion of dynamic effects makes it possible to determine the superconducting transition temperature, as well as the critical coupling constant for underdoped graphene, more accurately than in the static approximation of the BCS type. Estimates of the constants of electron interaction with the scalar optical phonon mode in graphene indicate that an appreciable superconducting transition temperature can be attained under a high chemical doping level of graphene.

The Role of Intravascular Intervention in the Management of Budd-Chiari Syndrome

To evaluate the efficacy of intravascular intervention in the management of different types of Budd-Chiari syndrome. Fifty-three patients of BCS were clinically diagnosed and interventionally treated in terms of their signs and symptoms of portal hypertension and occlusive inferior vena cava/or hepatic veins with the combination of Doppler ultrasonography, CT scan, and angiography. The interventional methods applied in this study included percutaneous transluminal angioplasty and IVC stent implantation (PTA+IVC stent); transjugular hepatic veno-stent placement (PTA+HV stent) or transjugular transluminal hepatic veno-inferior vena cava stent placement and transcaval transjugular intrahepatic portocaval shunt. The success rate of intravascular interventional therapy was 92.45% (49/53). After interventional therapy, the patients' pleural effusion, ascites, prominent veins formation of bilateral flanks or backs alleviated, hepatomegaly reduced, and the urinary output increased. The longest follow-up case was 13 years with patent stent. Two patients died of pulmonary embolization or pericardial tamponade during surgery. Intravascular intervention is a safe and effective therapy for most types of BCS.

Oxidized Mesoporous Silicon Microparticles for Improved Oral Delivery of Poorly Soluble Drugs

Surface functionalized mesoporous silicon (pSi) microparticles are reported as a solid dispersion carrier for improving dissolution and enhancing the orally administered pharmacokinetics (fasted rat model) of indomethacin (IMC), employed as a model poorly soluble BCS type II drug. IMC was loaded via immersion/solvent evaporation onto the thermally oxidized pSi particles, which provide a stable hydrophilic matrix with a nanoporous structure. The solid state properties of IMC loaded pSi were characterized by Fourier transform infrared spectroscopy, X-ray powder diffraction, differential scanning calorimetry and thermogravimetric analysis. IMC molecules are encapsulated in a noncrystalline state due to geometric confinement in the nanopores; stability of the noncrystalline state has been demonstrated for several months under accelerated storage conditions. The pSi carrier facilitates accelerated immediate release of IMC and enhanced oral delivery performance in comparison with crystalline indomethacin and Indocid i.e. a 4-times reduction on T(max), a 200% increase on C(max) and a significant increase in bioavailability. The in vitro-in vivo correlation is discussed based on the noncompartment model and gives insight into the delivery mechanism for the pSi carrier.

Superfluidity in atomic Fermi gases

In a trapped atomic Fermi gas, one can tune continuously via a Feshbach resonance the effective pairing interaction between fermionic atoms from very weak to very strong. As a consequence, the low temperature superfluidity evolves continuously from the BCS type in the weak interaction limit to that of Bose–Einstein condensation in the strong pairing limit, exhibiting a BCS–BEC crossover. In this paper, we review recent experimental progress in atomic Fermi gases which elucidates the nature of the superfluid phase as the interaction is continuously tuned. Of particular interest is the intermediate or crossover regime where the s-wave scattering length diverges. We will present an intuitive pairing fluctuation theory, and show that this theory is in quantitative agreement with existing experiments in cold atomic Fermi gases.

The electromagnetic response of a fermion system at zero temperature

An investigation is shown whether the Meissner-Ochsenfeld effect exists in a gas of spin 1/2 fermions in which an attraction (denoted by W) between particles having the same momenta and opposite spins as well as a BCS type four-fermion interaction between pairs are present in a system. The former potential is equivalent to the effective kinetic energy of free fermion pairs. The latter interaction (denoted by V 4 ) is responsible for the presence of fermion quadruples in the system. The Meissner effect proves to be weaker than in BCS theory, implying a larger penetration depth λ of the external magnetic field in the regime of the weak attraction W; however, this effect turns out to exist even when the gap parameter of quadruples vanishes. In this regime the strength of the Meissner effect is the same as in the BCS case.

The Bonn nuclear quark model revisited

We present the exact solutions to the equations of the lowest energy states of the colored and color-symmetric sectors of the Bonn quark model, which is SU ( 3 ) symmetric and is defined in terms of an effective pairing force with su ( 4 ) algebraic structure. We show that the groundstate of the model is not color symmetrical except for a narrow interval in the range of possible quark numbers. We also study the performance of the Glauber coherent state, as well as of superconducting states of the BCS type, with respect to the description, not only of the absolute (colored) groundstate, but also of the minimum energy state of the color-symmetrical sector, finding that it is remarkably good. We use the model to discuss, in a schematic context, some controversial aspects of the conventional treatment of color superconductivity.

Particle-number restoration within the energy density functional formalism

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.

Effect of external magnetic field on superconducting and spin density wave gaps of high- Tc superconductors

A theoretical model is addressed here to study the interplay of the superconductivity (SC) and the spin density wave (SDW) long range orders in underdoped region in the vicinity of on-set of superconductivity in presence of an external magnetic field. The order parameters are calculated by using Zubarev’s technique of Green’s functions and determined numerically self-consistently. The gap parameters are found to be strongly coupled to each other through their coupling constants. The interplay displays BCS type two gaps in the quasi-particle density of states (DOS) which resemble the tunneling conductance of STM experiments. The gap edges in the DOS appear at ± ( z + z 1 ) and ± ( z - z 1 ) . The applied magnetic field further induces Zeeman splitting which is explained on the basis of spin-filter effect of tunneling experiment.

BCS-BEC crossover and phase structure of relativistic systems: A variational approach

We investigate here the BCS-BEC crossover in relativistic systems using a variational construct for the ground state and the minimization of the thermodynamic potential. This is first studied in a four-fermion point interaction model and with a BCS type ansatz for the ground state with fermion pairs. It is shown that the antiparticle degrees of freedom play an important role in the BCS-BEC crossover physics, even when the ratio of Fermi momentum to the mass of the fermion is small. We also consider the phase structure for the case of fermion pairing with imbalanced populations. Within the ansatz, thermodynamically stable gapless modes for both fermions and antifermions are seen for strong coupling in the Bose-Einstein condensation (BEC) regime. We further investigate the effect of fluctuations of the condensate field by treating it as a dynamical field and generalize the BCS ansatz to include quanta of the condensate field also in a boson-fermion model with quartic self-interaction of the condensate field. It is seen that the critical temperature decreases with inclusion of fluctuations.

Far-infrared signature of the superconducting gap in intercalated graphiteCaC6

Terahertz reflectance spectra of the Ca-intercalated graphite ${\text{CaC}}_{6}$ reveal a superconducting gap below 11 K. The gap signature lacks a sharp onset to full reflectivity at $2{\ensuremath{\Delta}}_{0}$ but rather shows a distribution of gap values consistent with an anisotropic gap. The experimental data were successfully fitted to the gap distribution obtained from density-functional calculations of Sanna et al. [Phys. Rev. B 75, 020511(R) (2007)]. The temperature dependence of the superconducting gap is characteristic for a BCS type superconductor.

Pairing correlations and soft dipole excitations in nuclei on the neutron-drip line

Paring correlations and soft dipole excitations in weakly bound nuclei on the edge of neutrondrip line are studied by using a three-body model. A density-dependent contact interaction is employed to calculate the ground state of halo nuclei 6He and 11Li, as well as a skin nucleus 24O. Dipole excitations in these nuclei are also studied within the same model. We point out that the dineutron-type correlation plays a dominant role in the halo nuclei 6He and 11Li having the coupled spin of the two neutrons S = 0, while the correlation similar to the BCS type is important in 24O. Contributions of the spin S = 1 and S = 0 configurations are separately discussed in the low-energy dipole excitations. The calculated results are compared with recent experimental data of 6He and 11Li.

Critical temperature ofMgB2ultrathin superconducting films: BCS model calculations in the tight-binding approximation

We develop the multi-band BCS model of superconductivity in the ultrathin films using the orthogonal tight-binding approximation for constructing the electron wavefunctions. This allows for relatively simple determination of the band structure near the Fermi level as well as the electron-electron interaction matrix elements of the BCS type. The model is applied to the ultrathin MgB$_2$(0001) films, for which the critical temperature values are calculated in the thickness range 2...10 MgB$_2$ layers. The importance of the boundary conditions is emphasised, as either boron or magnesium layers may cover the film. It is found that films thinner than 4 layers show substantial decrease in the critical temperature. The charge spillage outside the geometric boundaries of the film, which is allowed in our model, suppresses $T_c$ oscillations and weakens its dependence on film covering layer composition.

Mesoscopic BCS pairing in the repulsive one-dimensional Hubbard model

We study mesoscopic pairing in the one-dimensional repulsive Hubbard model and its interplay with the BCS model in the canonical ensemble. The key tool is comparing the Bethe ansatz equations of the two models in the limit of small Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations with infinite pairing coupling are recovered; a finite pairing is obtained by considering a further density-dependent phase-correlation in the hopping amplitude of the Hubbard model. We find that spin degrees of freedom in the Hubbard ground state are arranged in a state of the BCS type, where the Cooper pairs form a noncondensed liquid on a ``lattice'' of single particle energies provided by the Hubbard charge degrees of freedom; the condensation in the BCS ground state corresponds to Hubbard excitations constituted by a sea of spin singlets.

Spatial structure of neutron Cooper pair in low density uniform matter

We analyze spatial structure of the neutron Cooper pair in superfluid low-density uniform matter by means of BCS calculations employing a bare force and the effective Gogny interaction. It is shown that the Cooper pair exhibits a strong spatial di-neutron correlation in a wide range of neutron density $\rho/\rho_0\approx 10^{-4}-0.5$. This feature is related to the crossover behavior between the pairing of the weak coupling BCS type and the Bose-Einstein condensation of bound neutron pairs. We also show that the zero-range delta interaction can describe the spatial structure of the neutron Cooper pair if the density dependent interaction strength and the cut-off energy are appropriately chosen. Parameterizations of the density-dependent delta interaction satisfying this condition are discussed.

Resistive studies of the pseudogap in YBCO films with consideration of the transition from BCS to Bose–Einstein condensation

A new approach is proposed for analysis of the excess conductivity σ′(T) arising below a characteristic temperature T*⪢Tc in YBa2Cu3O7−y (YBCO) films with different oxygen concentrations. The approach is based on the idea that σ′(T) is formed as a result of the formation at T⩽T* of local pairs (tightly bound bosons) obeying Bose–Einstein statistics in the temperature interval Tm<T<T*. At temperatures Tcmf<T<Tm the pairs obey BCS theory (Tcmf is the critical temperature separating the phase transition region from the region of critical fluctuations). Thus in Y123 systems a transition from Bose–Einstein condensation to condensation of the BCS type occurs with decreasing temperature. An equation in which the dynamics of formation of the tightly bound bosons is taken into account is proposed which gives a good description of the temperature dependence σ′(T) and in which the parameter Δ*, identified with the pseudogap in high-Tc superconductors, is contained in explicit form. The temperature dependence Δ*(T) is obtained for all the films studied.

The critical temperature of a superconductor on a possible mediated pairing mechanism

The possibility of pairing correlations arising from the quenching of the repulsiveelectron–ion Darwin term in the pairon (Cooper pair) state is examined. Twopairing processes, arising from ionic density fluctuations (phonons) and fromelectronic density fluctuations (excitons), are shown to dominate in lowTc andhigh Tc superconductors, respectively. Based on a two-body interaction potential the BCS type of wavefunction and reduced Hamiltonian are obtained. Asquenching occurs only when a pairon is scattered by the nucleus without recoil between an electronand a hole section of the Fermi surface, a two-band model with umklapp processes gives theTc equation for both the phonon- and exciton-coupled superconductors whose solution issimilar to that obtained by Eliashberg equations except that the dependence ofTc on structure is explicitly included.

Pairing correlations in nuclei on the neutron-drip line

Paring correlations in weakly bound nuclei on the edge of neutron drip line is studied by using a three-body model. A density-dependent contact interaction is employed to calculate the ground state of halo nuclei $^{6}$He and $^{11}$Li, as well as a skin nucleus $^{24}$O. Dipole excitations in these nuclei are also studied within the same model. We point out that the di-neutron type correlation plays a dominant role in the halo nuclei $^{6}$He and $^{11}$Li having the coupled spin of the two neutrons $S$=0, while the correlation similar to the BCS type is important in $^{24}$O. Contributions of the spin $S$=1 and S=0 configurations are separately discussed in the low energy dipole excitations.

Role of interlayer coupling on the isotope effect in layered high- Tc cuprate superconductors

The present work deals with the study of the role of interlayer coupling on the isotope effect in high- T c layered cuprate superconductors. For this purpose, we have considered two-layer tight-binding model that includes the intralayer attractive BCS type interactions and interlayer coupling in the form of single particle and Josephson Cooper pairing tunneling. Such a model calculation will be applicable for the high- T c cuprate system like YBa 2Cu 3O 7− x , having two CuO 2 plane per unit cell, and also several other cuprate materials and may be extended for multilayer cuprate systems. To calculate the isotope effect coefficient ( α), we derive the expression for the superconducting order parameter within the BCS mean field. We find that the isotope effect coefficient ( α) increases with single particle tunneling but is independent of the Josephson Cooper tunneling. Finally, we have explained our theoretical results on isotope effect coefficient in the light of existing experimental observations.