Calculation of the vortex structure in a superconducting alloy

We calculate properties of an isolated vortex in a dirty BCS superconductor at zero temperature by numerical integration of a diffusion equation. This is supplemented by a self-consistency equation for the order parameter, and we show that a simple trial form gives quite a good solution of it. The electronic density of states and low temperature specific heat are also calculated for extreme type II material. The difference between the density of states at frequencies ω and 0 is proportional to ω² for small ω, and the specific heat is similar to that predicted by previous approximate theory.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Specific heat jump in BCS superconductors

An exact analytical expression for the specific heat jump at the critical temperature T_c has been obtained directly from the BCS gap equation for any shape of the energy dependent electronic density of states (DOS). We consider a model which takes into consideration electron-electron repulsion, formulated in the Hubbard model along with the electron-electron attraction due to electron-phonon interaction in the BCS formalism. We have analyzed this expression for constant as well as for the Lorentzian forms of DOS. It is shown that the constant DOS in the simple BCS theory cannot explain the large values of , found in some superconductors. The specific heat versus temperature curve has been found to have a peak, similar to that of Eliashberg theory of superconductivity. The influence of repulsive interaction is very small and occurs mainly at higher temperatures. Received: 26 January 1998     

Nuclear level densities with collective rotations included

The level density is calculated from the single particle energies in a Woods-Saxon potential with pairing included in the BCS approximation. The collective rotations are included by addition of a rotational band on top of each of the intrinsic levels. The nuclei investigated have mass numbers in the region 100 ≦ A ≦ 253. At the ground state deformation and at the neutron separation energy for the nucleus in question we compare calculated and observed level densities. The dependence on the parameters in the model are investigated. Considering the uncertainties in these parameters the calculated results are believed accurate to within a factor of 3. The rotations contribute typically a factor of 40. They must be included for deformed and not for spherical nuclei. We underestimate systematically the level density by a factor of 4 with fluctuations around the average value by a factor of 3. The nuclei lighter than ¹³⁸Ba are an exception. We obtain around a factor 100 too few levels in the calculation.     

Specific features of the BCS-BEC crossover and thermodynamics in the 2D resonant Fermi gas with p-wave pairing

The 2D resonant Fermi gas with p-wave pairing is considered n the BCS-BEC regime. For the 2D analog of the superfluid A1 phase, the Leggett equations [1] for superfluid gap Δ and chemical potential μ are analytically solved at T = 0 and the spectrum of the collective excitations (acoustic waves) is analyzed in the BCS regime (μ > 0), where the triplet Cooper pairs emerge; in the BEC regime (μ < 0), where the triplet local pairs (molecules) emerge; and in the transition region, where μ → 0. At low temperatures, the contribution of the superfluid Fermi quasiparticles of the resonant gas to heat capacity C _v and the density of normal component ρ_n is also calculated. At μ = 0, the fermionic contribution to ρ_n and C _v are represented as power functions of temperature (ρ_n ～ T ³ and C _v ～ T ²). However, similar power contributions to these quantities are related to phonons (bosonic acoustic oscillations). The possibility of the experimental observation of the nontrivial topological term with the charge Q = 1 in the BCS regime of the 2D A1 phase is briefly discussed.     

A cellular model for the specific heat of amorphous solids at low temperatures

The wave equation for a non-homogeneous continuum with a statistical mass-density distribution is studied as a model for the vibrational specific heat of amorphous solids. The frequency spectrum is calculated for the simple case of small homogeneous cells separated from each other by hard and soft boundary walls distributed at random. The usual bulk mode density is enhanced by a positive constant term yielding the specific heat AT + BT³. From experimental values of the constants A, an upper limit of about 70 Å is calculated for the average cell diameter in vitreous SiO₂ and GeO₂.     

Specific Heat of the Spin-1/2 Dimerized Antiferromagnetic Chains at Low Temperatures

A spin linear chain with antiferromagnetic nearest-neighbor interaction is considered. The coupling constants of each spin with the right and left neighbors are different. Within the Bulaevskii model, the magnetic specific heat is calculated as a function of temperature for different alternation parameters. It is shown that the temperature dependence of the specific heat has two regimes. In the first one, the temperature is lower than half the band gap; in this case, in the low-temperature limit, C ∝ T^-1 exp(?Δ/k_BT). In the second regime, the temperature exceeds half the band gap; in this case, we approximately have C ∝ T.     

Modified BCS treatment of pairing correlations in 240Pu at high spin and finite temperature

Strutinsky calculations are used to investigate the shape and fission stability of rotating nuclei at finite temperature. Pairing correlations are described within a modified BCS approach which allows for the inclusion of both thermal and rotational degrees of freedom. Numerical results are discussed for the case of the deformed nucleus ²⁴⁰Pu up to angular momentum $\text{I = 40}\text{h}\text{?}$. The critical temperature T which characterizes the collapse of the pairing correlations is found to be of the order of T_c ≈ 0.40 MeV, for I = 0.     

LEVEL DENSITY AND FINITE-TEMPERATURE SPECIFIC HEAT OF NUCLEUS 104Pd UNDER MICROSCOPIC IBM

By using the microscopic sdgIBM-F_max approach, procedure of canonical ensemble average and saddle point approximation, thermodynamics of nucleus is established under microscopic IBM. Calculations of spectrum, level density and finite-temperature specific heat for the nucleus ¹⁰⁴Pd are carried out. The calculated values are coincident with the experimental data reported recently. The results predict that the shape phase transition in ground state band appears at about T≈0.230MeV and the phase transition of thermal excitation mode takes place at T≈0.630MeV for nucleus ¹⁰⁴Pd.     

The mass effects on two-dimensional relativistic fermions

We investigate chemical potential, internal energy and specific heat of ideal relativistic fermions in two spatial dimensions taking into account the finite mass effect and the finite carrier concentration. The results show that the heavy mass and low carrier concentration fermions trend to be non-relativistic. The light mass and high carrier concentration lead more relativistic behavior. For massless fermions, the total kinetic energy equals to a constant for a given density (n), which is a function of n^3/2. Meanwhile, the specific heat for massless fermions keeps the linear increasing behavior with temperature with constant slope rather than the slope of zero, which is deduced from the non-relativistic case.     

Specific heat anomaly of single phase YBa2Cu3O7-δ at superconducting transition temperature

The specific heat of single phase YBa₂Cu₃O_7-δ has been measured using non-adiabatic method between 4.2K and 120K. There is a specific heat anomaly Δc at 90K (about 3.2% of total specific heat) approximately, due to superconducting transition. From the measured value of ΔC and transition temperature T_c, the electronic density of state at Fermi level N(E_F) and Sommerfeld parameter γ calculated are 2.55±0.30states/eV.Cu-atom and 2.77±0.30 mJ/mole.K², respectively. The experimental result of N(E_F) is consistent with that of the band calculation by Mattheiss. The Debye temperature above T_c in this material deduced from Debye function is about 340K. Below 20K, the relation C=γ'T+βT³ is satisfied. But the value of γ' is smaller. That means, most of the electrons have formed superconducting Cooper pairs which give no contribution to specific heat below 20K.     

Manifestation of pairing effects in the cross section for 238Pu fission induced by neutrons

The cross section for ²³⁸Pu fission induced by neutrons with energies between 1 keV and about 5 MeV is described within the statistical model. It is shown that the stepwise structure observed above the fission threshold (at incident-neutron energies of Es>1 MeV) is due to the step in the level density of the fissile ²³⁹Pu nucleus at deformations corresponding to the inner fission barrier. In turn, the step in the level density of the odd nucleus ²³⁹Pu is associated with the excitation of internal single-and three-quasiparticle states. The level density is described with allowance for collective, pairing, and shell effects.     

Quasiparticle density of states of 2H-NbSe2 single crystals revealed by low-temperature specific heat measurements according to a two-component model

Low-temperature specific heat in a dichalcogenide superconductor 2H-NbSe2 is measured in various magnetic fields. It is found that the specific heat can be described very well by a simple model concerning two components corresponding to vortex normal core and ambient superconducting region, separately. For calculating the specific heat outside the vortex core region, we use the Bardeen-Cooper Schrieffer （BCS） formalism under the assumption of a narrow distribution of the superconducting gaps. The field-dependent vortex core size in the mixed state of 2H-NbSe2, determined by using this model, can explain the nonlinear field dependence of specific heat coefficient γ（H）, which is in good agreement with the previous experimental results and more formal calculations. With the high-temperature specific heat data, we can find that, in the multi-band superconductor 2H-NbSe2, the recovered density of states （or Fermi surface） below Tc under a magnetic field seems not to be gapped again by the charge density wave （CDW） gap, which suggests that the superconducting gap and the CDW gap may open on different Fermi surface sheets.     

Thermodynamic properties of superconducting nuclear matter

Phase diagrams of superconducting nuclear matter are calculated by solving a set of finite temperature gap equations, using several Skyrme effective interactions. Our results indicate that nuclear matter may have a superconducting phase in a small region with density near one half of the normal nuclear matter density and temperature k_BT ≲ 1.4 MeV. Our calculation is based on a finite temperature Green's function method with an abnormal pair cutoff approximation. The same approximation is employed in deriving the internal energy, entropy and chemical potential of superconducting nuclear matter. In this way, its equation of state is obtained, and compared with that of normal nuclear matter. The energy gap of superconducting nuclear matter is found to depend rather sensitively on both density and temperature. This dependence is analysed in terms of the Skyrme interaction parameters. The correlation effect on chemical potential is found to be important at high density, and its inclusion is essential in determining the equation of state of superconducting nuclear matter.     

Microcanonical ensemble study of a gas column under gravity

The study of a classical ideal gas column of finite height H in a uniform gravitational field g is made by the microcanonical ensemble at energy E. The primary functions of this ensemble, the phase volume and the density of states, are derived. Related statistical quantities, such as the entropy, the temperature and the heat capacity, are also reported. The equivalence in the thermodynamic limit between the calculated microcanonical expressions and those obtained from the canonical ensemble is shown numerically. The expression for the temperature is used to analyze the temperature change when the gas is permitted to expand into an evacuated region increasing the height of the column from H ₁ to H ₂. The microcanonical single-particle momentum and height distributions are also reported.     

Specific heat of a BCS superconductor

By expressing the free energy as an appropriate temperature integration over the square of the BCS energy gap function and by substituting simple but accurate analytic expressions for the latter, corresponding expressions are obtained for the specific heat in the superconducting state. In the upper portion of the temperature range, the ratio of the specific heats in the superconducting and normal states is 2.43 (1 + 0.936 in t), to better than one per cent accuracy, where t is the reduced temperature. Thus, the semilog plot of temperature versus the ratio of specific heat to temperature is a straight line over a large portion of one decade of specific heat. Corresponding expressions of similar simplicity and accuracy are obtained for the middle and low temperature ranges.     

Specific heat of a Kondo superconductor: (La, Ce) Al2

The specific heat of LaAl₂ and (La_1-xCe_x)Al₂ (x ? 0.0064) has been measured between 0.3 and 5 K, both in the superconducting and in the normal state. For all samples the same values for the Debye temperature as well as for the electronic specific heat coefficient have been determined. LaAl₂ shows an excellent BCS behavior. A remarkable excess specific heat at low temperatures due to the Kondo effect has been observed for all superconducting as well as for the normal conducting (La_1-xCe_x) Al₂ alloys. The specific heat jump ΔC at T_c depressed rapidly with increasing Ce concentration, allows the Kondo temperature T_K ? 1 K to be determined. ΔC vanishes at finite temperatures.     

Excitations électroniques dans les supraconducteurs purs de 2ème espèce

In a pure superconductor of the second kind, with a??1, one can consider the region far from vortex lines as a BCS superconductor with a local superfluid velocity. We calculate the local density of states due to the excitations in such a superconductor, then the density of states of the excitations for the whole superconductor, except for the core regions. This density of states remains finite even near the gap and takes a non-zero value below the gap.     

Effect of Dzyaloshinskii−Moriya interactions on Kagome anti-ferromagnetic clusters

The low energy and low temperature behavior of a few finite size Kagome clusters, including mixed spin systems of S=1/2 and S=1, with the nearest neighbor Heisenberg antiferromagnetic model is studied under the influence of out-of-plane Dzyaloshinskii?Moriya interactions (DMI) within the exact diagonalization formalism. The ground state of all the finite size systems is found to be present in the lowest spin sector with a finite gap to the lowest magnetic excitation irrespective of the strength of out-of-plane DMI. The energy level structures within the non-magnetic ground state and the lowest magnetic state have been studied for all the systems as a function of DMI. The characteristic signature of such low-lying non-magnetic excitations is reflected in the low temperature behavior of the specific heat. It is also found that the ground state chiral structure (characterized by the vector chiral order of the system) in the xy-plane shows sharp changes as a function of out-of-plane DMI at level crossing or avoided crossing regions. The in-plane spin ordering for each system is also studied with the estimation of static structure factor as a response to the varying strength of DMI.