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 the Ca-intercalated graphite superconductor CaC6

The superconducting state of Ca-intercalated graphite CaC6 has been investigated by specific heat measurements. The characteristic anomaly at the superconducting transition (Tc = 11.4 K) indicates clearly the bulk nature of the superconductivity. The temperature and magnetic field dependence of the electronic specific heat are consistent with a fully gapped superconducting order parameter. The estimated electron-phonon coupling constant is lambda = 0.70 +/- 0.04, suggesting that the relatively high Tc of CaC6 can be explained within the intermediate coupling BCS approach.     

Specific heat of the non-centrosymmetric superconductor Re3W

The alloys of non-centrosymmetric superconductor, Re 3 W, which were reported to have an α-Mn structure [P. Greenfield and P. A. Beck, J. Metals, N. Y. 8, 265 (1959)] with T c = 9 K, are prepared by arc melting. The values of ac susceptibility and the low-temperature specific heat of these alloys are measured. It is found that there are two superconducting phases coexisting in the samples with T c1 ≈ 9 K and T c2 ≈ 7 K, which are both non-centrosymmetric in structure as reported previously. By analysing the specific heat data measured in various magnetic fields down to a temperature of 1.8 K, we find that the absence of the inversion symmetry does not lead to an obvious deviation from an s-wave pairing symmetry in Re 3 W.     

Specific heat of the electronic superconductor Pr1.85Ce0.15CuO4

We have investigated the specific heat of the ceramic Pr_1.85Ce_0.15CuO₄ in the temperature range 2–800K in magnetic fields up to 8 T. We have determined the magnitude of the specific-heat discontinuity at the superconducting transition ΔC/T _c and estimate the coefficient of the electronic specific heat. In the temperature interval 5–800K we have separated out the phonon contribution to the specific heat, determined the temperature dependence of the characteristic Debye temperature Θ, and calculated the mean frequencies (moments) of the phonon spectrum. We compare the parameter values obtained in this way with data for the compound La_1.85Sr_0.15CuO₄ having similar crystal structure, but hole conductivity. The magnitude of the specific-heat discontinuity and consequently the effective electron mass in the “electronic” superconductor Pr_1.85Ce_0.15CuO₄ is several times smaller than in the “hole” superconductor La_1.85Sr_0.15CuO₄. The phonon spectrum in Pr_1.85Ce_0.15CuO₄ in the low-energy region is somewhat “more rigid,” and in the high-energy region somewhat “softer” than in La_1.85Sr_0.15CuO₄. Fiz. Tverd. Tela (St. Petersburg) 41, 1154–1159 (July 1999)     

Specific heat of Tb x Y1−x Sb mixed crystals

The specific heat of Tb _x Y_1?x Sb mixed crystals (x=0, 0.103, 0.383, 0.428, 0.467, 0.635, 0.928 and 1.0) has been measured between 1.6 and 20°K using an adiabatic calorimeter. The crystal field potential is described well taking into account only 4th order terms, and the overall splitting of the ground multiplet⁷F₆ of the Tb³⁺ ion has been found to be 115°K independent of the concentrationx. Forx>0.46 the specific heat curves exhibit a behaviour typical for a second order phase transition. For lower concentrations a normal Schottky anomaly is found and no evidence for magnetic order was detected. The experimental results which are in agreement with magnetic measurements are compared with molecular field calculations including crystal field and exchange interaction.     

Tunneling density of states of the Kondo superconductor (La1−x Ce x )Al2

Tunneling measurements on (La_1?x Ce _x )Al₂ single crystals (x=0; 0.001; 0.002) were performed at 0.1 K. Heavily dopedp-type GaAs/Zn acts as normal conducting counterelectrode where the Schottky-barrier provides the insulating layer for tunneling. Contact between counterelectrode and sample surface is not made before cooling down to 1 K. Contamined surface layers can be pierced mechanically at 0.1 K. The extremely gapless behaviour agrees with an impurity band positiony ₀<0.8 for localized exited states, although no detailed structure can be resolved.     

Specific heat and lattice dynamics of layered TiS2 crystal

The specific heatC of the layered 1T-CdI₂ type TiS₂ crystal has been measured over the temperature range 20–300 K using a thermal relaxation method. Based on the available information about lattice dynamics for acoustic and optical phonon modes in TiS₂, the dispersion curve and the density of states for each mode are evaluated using a simplified phonon Brillouin zone of a cylindrical form. The calculatedC-T curve is in good agreement with the observation.     

Local measurement of the superfluid density in the pnictide superconductor Ba(Fe(1-x)Co(x))(2)As(2) across the superconducting dome

We measure the penetration depth λab(T) in Ba(Fe(1-x)Co(x))(2)As(2) using local techniques that do not average over the sample. The superfluid density ρs(T) ≡ 1/λab(T)2 has three main features. First, ρs (T = 0) falls sharply on the underdoped side of the dome. Second, λab(T) is flat at low T at optimal doping, indicating fully gapped superconductivity, but varies more strongly in underdoped and overdoped samples, consistent with either a power law or a small second gap. Third, ρs (T) varies steeply near Tc for optimal and underdoping. These observations are consistent with an interplay between magnetic and superconducting phases.     

Specific heat of the semiconducting layered compound SnSe2 at low temperatures

The specific heat of the layer compound semiconductor tin diselenide SnSe₂ has been measured in the temperature range from 2.7 to 280 K. In this range, the overall temperature dependence of the specific heat is dominated by the lattice contribution, which yields a limiting Debye characteristic temperature at absolute zero θ_D (0) = 140 ± 2K. The increase in the specific heat at low temperatures is more gradual than what would be expected for a simple Debye solid, and reflects the quasi-two dimensional layer structure of this compound.     

Observation of the Meissner effect in polysulphur nitride, (SN)x

The superconductivity of (SN)_x is definitely established by the observation of a Meissner effect with the magnetic field applied perpendicular and parallel to the (SN)_x fibre axis. Considerable flux trapping is observed and the magnetization curves are similar to those expected for coupled filamentary type II superconductors.     

Angle-resolved photoemission study of the cobalt oxide superconductor Na(x)CoO(2) x yH(2)O: observation of the Fermi surface

The cobalt oxide superconductor Na(x)CoO(2) x yH(2)O is studied by angle-resolved photoemission spectroscopy. We report the Fermi surface (FS) topology and electronic structure near the Fermi level (E(F)) in the normal state of Na(x)CoO(2) x yH(2)O. Our result indicates the presence of the hexagonal FS centered at the Gamma point, while the small pocket FSs along Gamma-K direction are absent, similar to Na(x)CoO(2). The top of the e(g)(') band, which is expected in band calculations to form the small pocket FSs, extends to within approximately 30 meV below E(F), closer to E(F) than in Na(x)CoO(2). We discuss its possible role in superconductivity, comparing with other experimental and theoretical results.     

Theory of the high-frequency chiral optical response of a p(x) + ip(y) superconductor

The optical Hall conductivity and the polar Kerr angle are calculated as functions of temperature for a two-dimensional chiral p(x) + ip(y) superconductor, where the time-reversal symmetry is spontaneously broken. The theoretical estimate for the polar Kerr angle agrees by the order of magnitude with the recent experimental measurement in Sr2RuO4 by Xia et al. [Phys. Rev. Lett. 97, 167002 (2006)10.1103/PhysRevLett.97.167002]. The theory predicts that the Kerr angle is proportional to the square of the superconducting energy gap and is inversely proportional to the cube of frequency, which can be verified experimentally.     

X-ray spectra and electronic structure of Li x NbO2 superconductor and other niobium oxide compounds

X-ray emission Nb and OK spectra and O1s total photoelectron yield spectra for superconductor Li_0.71NbO₂ and other niobium oxide compounds NbO, BaNb₄O₆, Ba₂Nb₅O₉, BaNb₅O₈. LiNbO₂, NbO₂, LiNbO₃ were investigated. It was found that in stoichiometric LiNbO₂, niobium oxidation degree is 3+. Under the lithium deintercalation down to Li_0.71NbO₂ composition, the niobium ions oxidation degree increases up to 3.3+. As more electrons are supplied by Nb to fill the O2p band, the degree of O2p-Nb4d hybridization is increased. Using the full-potential linear muffin-tin orbital method, the self-consistent band structure calculations of Li _x NbO₂ (x=1.0; 0.7; 0.5) compounds were carried out. Agreement between partial Nb4d and O2p densities of states and corresponding X-ray spectra was observed. For thex=0.7; 0.5 the Fermi level is placed on the slope of sharp density of states peak formed mostly by the Nb4d states. With the decrease ofx thep-d hybridization becomes stronger, although remains well below the values typical for the high-temperature superconductors.     

Unconventional superconductivity in electron-doped layered Li0.48(THF)yHfNCL.

We report magnetic susceptibility measurements on a layered superconductor Li0.48(THF)0.3HfNCl having Tc approximately 26 K. The present study revealed that (a) the Fermi level density of states is small, N*(EF) approximately 0.25 states/(eV spin f.u.), (b) mass enhancement is negligible, gamma; approximately 1, (c) electron-phonon coupling is weak, lambda(ep)<1, (d) exchange enhancement is negligible, 1/(1+F(a)0) approximately 1, and (e) electronic density parameter is large, r(2D)s approximately 10.3 (i.e., low-carrier density). It is difficult to explain the origin of the high Tc in terms of the conventional phonon (BCS) mechanism of superconductivity.     

Specific heat anomaly in the 90 K superconductor HoBa2Cu3O7−y

We report here the results of our heat capacityC _p measurements on a monophasic material HoBa₂Cu₃O_7−y . ΔC _p/T_c, the jump inC _p at the superconducting transition temperature (=91 K) of the material is measured to be 31 mJ/mol-K².