BCS Pairing Theory Research Articles

Ground State Properties and Shape Transition of Even-Even 76Os, 78Pt, 80Hg and 82Pb Isotopes in the Framework of Skyrme Hartree-Fock-Bogoliubov Theory

The Hartree-Fock-Bogolyubov (HFB) theory is a good theoretical approximation for describing the nuclear structure of neutron-rich deformed nuclei, it is generalized the HF theory with BCS pairing theory. In this work, ground-state properties of even-even 76Os, 78Pt, 80Hg and 82Pb isotopes from proton drip-line to neutron drip-line have been studied in the framework of the axially deformed Hartree-Fock-Bogoliubov (HFB) method with two Skyrme nucleon-nucleon force HFB9 and UNE1. The numerically calculated results of binding energy, two neutron separation energy, two neutron shell gap, quadrupole deformation, neutron pairing gap and charge radius are discussed and compared with the available values of the experiment, Finite Range Droplet Model (FRDM), Relativistic Mean-Field (RMF) and Hartree-Fock-Bogoliubov based on D1S Gognay force. The energy surface curves are plotted for some isotones of the investigated nuclei, the transition in the shapes was clear with the change in the number of neutrinos. Our calculations show good agreements in comparison with other data and results.

Neutron Skin Thickness of the Even-Even 124-208Sm Isotopes

Everything in the universe is made up of atoms, which are mediated by the nucleus. The understanding of the complex structure of the nucleus of atoms is still one of the major challenges. Therefore, the physics of rich neutron nuclei is one of the most subjects in nuclear structure physics both theoretically and experimentally. The Hartree-Fock-Bogolyubov (HFB) theory has a good theoretical framework for describing these nuclei since it is generalized the Hartree-Fock approximation with BCS pairing theory. In this work, the neutron skin thickness and neutron distribution, proton and neutron radii of the even-even 124-208Sm (Z=62) isotopes were calculated in the framework of the HFB calculations with three different Skyrme type effective nucleon-nucleon interaction: SKI3, HFB9, UNE1 and Gogny force of type D1S. In view of existing different type of models and interactions, the question remains which of them provide the best description of data. Our calculated values were compared with the available experimental and theoretical results, where good agreements were obtained.

ROTATIONAL BANDS IN HEAVY AND SUPERHEAVY NUCLEI WITHIN THE LUBLIN STRASBOURG DROP + YUKAWA FOLDED MODEL

The potential energies of heavy and superheavy even even nuclei were found within the macroscopic–microscopic method with LSD model, Yukawa–folded mean field, Strutinsky shell correction and BCS pairing theory in order to calculate the rotational state with cranking moments of inertia. The calculations were performed for a couple of nuclei: 250 No - 264 Hs on a deformation grid c = 0.8 up to 1.6 with step length 0.05 and h = -0.4 to 0.4 with step length 0.1. The equilibrium deformations were found and the masses compared to the experimental ones. Rotational energies of No isotopes for L/ħ = 2, 4, 6, 8, 10, 12 agree well with the data when a pairing strengths [Formula: see text] and a pairing window of [Formula: see text] levels is used. A prediction of the E2+ rotational states for all the investigated nuclei is given.

Unusual electron–phonon superconductivity in nickel borocarbides?

We propose a picture of incomplete superconducting condensation, which is based on the BCS pairing theory, to account for the seemingly contradictory observation of unconventional superconducting state properties including specific heat, magnetic penetration depth, spin–lattice relaxation rate, thermal conductivity, and microwave conductivity in nickel borocarbide superconductors RNi 2B 2C (R=Y, Lu), in which strong electron–phonon interaction plays an important role. We show that the power-law temperature T dependence of these properties at low T can arise in s-wave superconductors when a small fraction of charge carriers remain unpaired at T=0.

Bogoliubov-quasiparticle spectra of the effectived-wave model for cuprate superconductivity

An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective fermion model, a fictious model of hole quasiparticles derived from numerical studies of the two-dimensional t-J model at low doping. We show that there is actually a reasonable range of parameter values where the $d_{x^2-y^2}$-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap parameter of a size $\Delta_d\simeq 0.13|V|$ (where $V$ is the attractive interaction between holes) is estimated at low doping levels. The paired state gives way to the state of clustering of holes for some stronger attractions.

Excitation spectra of an effective d-wave model for cuprate superconductivity

An exact-diagonalization technique on finite-size clusters is used to study the ground states and some excitation spectra of the two-dimensional effective Fermi-liquid model derived from numerical studies of the t- J model. We show that there is actually a reasonable range of parameter values where the d-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory but that the clustering of holes rather easily occurs for some stronger attractions.

Electronic Pairing in Exotic Superconductors

Investigations of rare earth, Aactinide, organic and oxide compounds have yielded several new classes of exotic superconductors. These include magnetically ordered superconductors, A15 superconductors, buckyball superconductors, heavy-electron superconductors, organic superconductors and high-Tc oxide superconductors. These materials have properties significantly different from those of conventional superconductors such as Al and Zn, which are described well by the Bardeen-Cooper-Schrieffer model of superconductivity. We carefully distinguish between the BCS model and the more general BCS theory. In the BCS theory superconductivity arises, loosely speaking, from electron pairs that behave essentially as bosons and undergo macroscopic condensation to the lowest energy state at the critical temperature Tc The BCS model, presented in 1957, further specifies that the pairing is mediated by exchange of quantized lattice vibrations (phonons) between the electrons, yielding pairs with zero spin S (spin singlet) and zero angular momentum L (s wave). This model is but one example of the BCS pairing theory; another describes the superfluid state of 3He, where the fermionic 3He atoms form p-wave (L = 1) spin-triplet (S = 1) pairs held together by the exchange of magnetic excitations of the surrounding atomic sea.

Excitations and superconductivity in the two-dimensional t- J model

An exact-diagonalization technique on small clusters is used to study excitation spectra and superconductivity in the two-dimensional t- J model. We demonstrate that the low-lying excitations in a wide parameter ( J/ t) and doping regions of the model are described well by the picture of dressed Bogoliubov quasiparticles within the BCS pairing theory. The pairing occurs predominantly in d x 2− y 2 -wave channel and the energy gap has a size Δ d⋍0.15J−0.27J between quarter and half fillings.

Pairing theory of high Tc and low Tc superconductors

New solutions for T c, the order parameter, and the density of states are obtained, based on the fact that pairs are formed within the pairing interaction range, T D (Debye), via the BCS pairing theory (not the BCS results). They are valiid for all ify = T D πT c , and are applicable to low T c (LTC) and high T c (HTS) superconductors. The order parameter variation with y is shown to account for all features of HTS. A new density of states via the zero order parameter outside the pairing interaction range is found to account for low energy states observed in HTS. For large y (LTS), the BCS results are reproduced.

Bogoliubov quasiparticle excitations in the two-dimensional t-J model.

Using a proposed numerical technique for calculating anomalous Green's functions characteristic of superconductivity, we show that the low-lying excitations in a wide parameter and doping region of the two-dimensional $t$$-$$J$ model are well described by the picture of dressed Bogoliubov quasiparticles in the BCS pairing theory. The pairing occurs predominantly in $d_{x^2-y^2}$-wave channel and the energy gap has a size $\Delta_d$$\simeq$$0.15J$$-0.27J$ between quarter and half fillings. Opening of the superconducting gap in the photoemission and inverse-photoemission spectrum is demonstrated.

Topological frustration can lead to superconductivity

The author analyses charge motion in geometries composed solely of interconnecting 'diamonds'. Since a diamond is composed of two edge-sharing triangles, these geometries are topologically frustrated. The motion of a single particle across atoms which have restricted valence leads to a type of paramagnetism with only short range correlations in these geometries. When two particles meet in a diamond their behaviour is more bosonic than fermionic, which leads to a form of BCS pairing theory. The attraction can be interpreted as the pair locally unfrustrating the geometries and a resulting local regaining of lost kinetic energy leads to the attraction.

Identification of odd-parity superconductivity in UPt3 from paramagnetic effects on the upper critical field.

We present a theoretical explanation of the unusual temperature-dependent anisotropy of ${\mathit{H}}_{\mathit{c}2}$ reported by Shivaram et al. for single crystals of ${\mathrm{UPt}}_{3}$, which we argue provides strong support for unconventional odd-parity pairing. We show that the observed low-temperature crossover in the anisotropy ratio, ${\mathit{H}}_{\mathit{c}2}^{\mathrm{\ensuremath{\perp}}}$/${\mathit{H}}_{\mathit{c}2}^{\mathrm{?}}$, can be explained by paramagnetic limiting for H parallel to the sixfold axis within BCS pairing theory if the order parameter has odd parity and there is strong spin-orbit coupling of the pair spin to the crystal axes.

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 \(2\Delta (\hat k)\) can be quite different for \(\hat k\) 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 \(2\Delta _t (\hat k_t )\), wherekt is the wavevector in the plane of the layers.

Critical temperature in high T c layered superconductors: Dependence on structure and number of interacting conducting layers per unit cell

A simple model of intra- and inter-layer coupling based on a generalized BCS pairing theory of layered superconductors is used to correlate the T c's of a large number of systems with varied structures, in terms of the ration of inter- and intra-layer coupling strengths. The largest T c attainable by asymptotically increasing the number of layers is found to be about 143K in a model describing T l 1- and T l 2-systems, and 136.5K in the Bi 2-system.

Anisotropic superconductivity in high-T c layered crystals

The new high-T c superconductors have layered structures with anisotropic coherence lengths small compared to the normal state carrier mean free path ℓ. It is shown that the anisotropy of the energy-gap function of the generalized BCS pairing theory for layered materials with nonspherical Fermi surface, plays a crucial role in determining many of their properties in the superconducting state. The usual comparison of experimental results with the one-parameter isotropic BCS model is thus quite misleading in such cases. It is argued that single-crystal results on the low-temperature electronic specific heat and infrared absorption may be understood in terms of possible anisotropies in the gap function and the Fermi surface.

Pairing mechanisms and anisotropic superconductivity in layered crystals

Abstract A brief outline of the generalized BCS pairing theory is presented. The pairing of carriers can be due to the exchange of lattice-phonons or due to the exchange of electronic charge-density and spin-density excitations. It is argued that anisotropic physical properties in the normal as well as superconducting states in the new high-Tc materials are crucual in the development of any realistic theoretical approach, and in comparison of experimental results with correct BCS predictions involving superconductivity in layered crystals. The possibility of the break-down of the mean-field approximation is also discussed. As of now, the generalized BCS pairing approach is the only realistic microscopic theory available which may be applied to high-Tc superconductors.

Microscopic model for high-Tc oxide superconductors.

We report results of a BCS-pairing theory of high-{ital T}{sub {ital c}} superconductors based on a model using interlayer charge-transfer excitation as the intermediate boson. We apply the model specifically to YBa{sub 2}Cu{sub 3}O{sub 7}. The relevant electronic band structure is calculated analytically using the tight-binding approximation, which is in agreement with numerical results. A specific interlayer charge-transfer excitation is identified. The Eliashberg equations are solved in the Kirzhnits-Maksimov-Khomskii approximation to obtain {ital T}{sub {ital c}} and the gap {Delta}. We find 2{Delta}/{ital KT}{sub {ital c}}{similar to}10--14, and {ital T}{sub {ital c}} increasing exponentially with a decrease in the Cu(2)-O(4) bond length. These results are in general agreement with some recent experiments.

Excitation energy at scission in thermal-neutron-induced fission

For the thermal-neutron-induced fission of $^{235}\mathrm{U}$ and $^{233}\mathrm{U}$, we extract the internal excitation energy at the scission point by use of two different methods. The first method uses experimental data for $^{235}\mathrm{U}$ + ${n}_{\mathrm{th}}$ on the neutrons and gamma rays emitted from doubly magic fission fragments, where the extra stability associated with shell closures makes the deformation energy small. Under the assumption that both fragments have equal temperatures, this yields an upper limit of 9.9 MeV for the total internal excitation energy at scission. The second method uses experimental data for $^{233}\mathrm{U}$ + ${n}_{\mathrm{th}}$ on odd-even effects in fission-fragment mass distributions and yields an average value of 5.6 MeV for the total internal excitation energy at scission when integrated over all fission-fragment kinetic energies. In both cases the internal excitation energy at scission is significantly smaller than that predicted by the one-body-dissipation theory of Swiatecki and co-workers and is instead much closer to that predicted by ordinary two-body viscosity.NUCLEAR REACTIONS, FISSION $^{235}\mathrm{U}$ + ${n}_{\mathrm{th}}$, $^{233}\mathrm{U}$ + ${n}_{\mathrm{th}}$; extracted internal excitation energy at scission point. Neutrons and gamma rays from doubly magic fission fragments, odd-even effects in fission-fragment mass distributions, one-body dissipation, two-body viscosity, temperature-dependent BCS pairing theory.

Quasiclassical Green's function in the BCS pairing theory

We study a generalization of the quasiclassical Green's function which allows us to include the transfer of momentum to the particles. In this approach, we may handle Galilei transformations, rotations, and gauge transformations in a systematic way. As an example, we calculate the quasiparticle flow pattern which arises during the motion of the orbital vector in the ABM phase, and discuss the meaning of the intrinsic angular momentum of the Cooper pairs. Finally, we consider charged particles in a magnetic field, and derive a Boltzmann equation for a superconductor which applies to the Hall effect in the case of moving vortices.

Quasiclassical green's function in the BCS pairing theory

Abstract We develop a generalization of the quasiclassical Green's function which allows us to include the transfer of even small amounts of momentum to the particles. We explain the general principle and add a few illustrations.