Superconductivity Theory and Applications Part 2 ppt

Superconductivity – Theory and Applications 14 Varma, C. M. (1988). Missing valence states, diamagnetic insulators, and superconductors. Phys. Rev. Letters; 61, 23, pp. 2713-2716 Wu, M. K.; Ashburn J. R.; Torng, C. J.; Hor, P.H.; Meng, R. L.; Goa, L.; Huang, Z. J.; Wang, Y. Q. & Chu, C. W. (1987). Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu- O compound system at ambient pressure. Phys. Rev. Letters, 58, 9, pp. 908-910 Yang, J.; Li, Z. C.; Lu, W.; Yi, W.; Shen, X. L.; Ren, Z. A.; Che, G. C.; Dong, X. L.; Sun, L. L.; Zhou, F. & Zhao, Z. X. (2008). Superconductivity at 53.5 K in GdFeAsO 1−δ . Superconductor Science Technology, 21, 082001, pp. 1-3 Zhang, H. & Sato, H. (1993). Universal relationship between T c and the hole content in p- type cuprate superconductors. Phys. Rev. Letters, 70, 11, pp. 1697-1699 1. Introduction Two different ground states, superconductivity and magnetism, were believed to be incompatible, and impossible to coexist in a single compound. The Ce bas ed heavy Fermion superconductor CeCu 2 Si 2 , however, was discovered in the vicinity of magnetic phase Steglich et al. (1979). This new cl ass of superconductors, which are referred to as "unconventional" superconductor, demonstrate various novel properties which are not accounted for in the framework of the BCS theory. Electrons in unconventional superconductors are strongly correlated through the Coulomb interaction, while strong electron-electron correlations are not preferable for the conventional B CS superconductors. Modern theory predicts that the repulsive Coulomb interaction can induce attractive interaction to form superconducting Cooper pairs as the result of many-body effect Unconventional superconductivity is often observed nearby a quantum critical point (QCP), where magnetic instability is suppressed to T = 0 by some physical parameters. It is invoked that the quantum critical fluctuations, which are enhanced around QCP, drive the superconducting pairing interactions, instead of the electron-phonon interaction proposed in the BCS theory. In addition to the novel pairing mechanisms, unconventional superconductivity shows various novel superconducting states, such as Fulde-Ferrell-Larkin-Ovchinnikov state and spin-triplet pairing state. Unveiling novel mechanism and resulting novel properties is the main topic of condensed matter physics. The cobaltate compound is also classified to an unconventional superconductor when we take the results of nuclear spin-lattice relaxation r ate Fujimoto et al . (2004); Ishida et al. (2003), and specific heat Yang et al. ( 2005) measurements into account. A power-law temperature dependence, observed for both physical quantities i n the superconducting state, yields the existence of nodes (zero gap with sign change) on the superconducting gap, and ad dresses the unconventional pairing mechanism. Besides, a magnetic instability was found in the sufficiently water intercalated cobaltates Ihara, Ishida, Michioka, Kato, Yoshimura, Takada, Sasaki, Sakurai & Ta kayama-Muromachi (2005). The close proximity of superconductivity to magnetism in cobaltates lead us to consider that the same situation as heavy Fermion superconductors is realized in cobaltates. 0 Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 ·yH 2 O Yoshihiko Ihara 1 and Kenji Ishida 2 1 Department of Physics, Faculty of Science, Hokkaido university 2 Department of Physics, Graduate School of Science, Kyoto university Japan 2 2 Will-be-set-by-IN-TECH Fig. 1. Crystal structures of non-hydrate, mono-layer hydrate and bilayer hydrate compounds. In this chapter, the relationship between superconductivity and magnetism will be explored from the nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) experiments on superconducting and magnetic cobaltate. The principles of experimental technique is briefly reviewed in §3. Then the experimental results are presented in the following sections, §4 and §5. Finally, we will discuss the superconducting paring mechanisms in bilayer-hydrate cobaltate, showing the similarity between cobaltate and heavy Fermion superconductors. 2. Water induced superconductivity in Na x (H 3 O) z CoO 2 ·yH 2 O Superconductivity in a cobalt oxide compound was discovered in 2003 Takada et al. (2003). The hydrous cobaltate Na x (H 3 O) z CoO 2 · yH 2 O demonstrates superconductivity when water molecules are sufficiently intercalated into the compound by a soft chemical procedure. In contrast, anhydrous Na x CoO 2 does not undergo superconducting transition at l east above 40 mK Li et al. (2004). A peculiarity of superconductivity in Na x (H 3 O) z CoO 2 ·yH 2 Ocompound is the necessity of sufficient amount of water intercalation between the CoO 2 layers, and depending on the water content, superconducting transition temperatures vary from 2 K to 4.8 K. This compound is the first superconductor which shows superconductivity only in the hydrous phase. The cobaltate compound has three types of crystal structures with different water concentrations as shown in Fig. 1. The parent compound Na x CoO 2 ,whichisy = 0 and z = 0, contains the randomly occupied Na layer between the CoO 2 layers. When Na ions are deintercaleted and water molecules are intercalated between the CoO 2 layers, the crystal structure changes to bilayer hydrate (BLH) structure, in which the Na layer is sandwiched with double water layers to form H 2 O-Na-H 2 O block layer. Due to the formulation of this thick block layer, the CoO 2 layers are separated by approximately 10 Å, and is considered to have highly two-dimensional nature. Superconductivity is observed in this composition below 5 K. The crystal structure of the superconducting BLH compound changes to mono-layer hydrate (MLH) structure, which forms Na-H 2 O mixed layers between the CoO 2 layers containing less water molecules than those of BLH compounds. The water molecules inserted between CoO 2 layers are easily evaporated into the air at an ambient 16 Superconductivity – Theory and Applications Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 ·yH 2 O3 condition, seriously affecting the physical properties, namely superconductivity, of BLH compounds. A BLH compound left in the vacuum space for three days becomes a MLH compound, and does not demonstrate superconductivity. Inversely the crystal structure of the MLH compound stored in high-humid atmosphere comes back to the BLH structure, and superconductivity recovers, although the transition temperature of the BLH compound after the dehydration-hydration cycle is lower than that of a fresh BLH compound. Superconducting and normal-state properties in various kinds of samples have been investigated with several experimental methods. In the nor mal state, spin susceptibility is almost temperature independent above 100 K, which is a unique behavior irrespective of samples. The sample dependence appears below 100 K, for instance, spin susceptibility increases with decreasing temperature in some samples, but some do not. From the temperature dependence of spin susceptibility below 100 K, temperature independent susceptibility χ 0 , effective moment μ eff and Weiss temperature Θ W were reported to be χ 0 = 3.02 ×10 −4 emu/mol, μ eff ∼ 0.3 μ B and Θ W = −37 K by Sakurai et al. (2003). Different values are reported by Chou, Cho & Lee (2004), where the increase of susceptibility toward low temperature is hardly observed, and correspondingly, μ eff is rather small. Although the low temperature behavior of susceptibility is strongly sample dependent, we believe that the slight increase below 100 K is an intrinsic behavior because it is observed in most of the high-quality powder samples and also observed in the Knight shift measured by nuclear magnetic resonance Ihara, Ishida, Yoshimura, Takada, Sasaki, Sakurai & Takayama-Muromachi (2005) and muon spin rotation measurements Higemoto et a l. (2004). In the superconducting state, specific heat is intensively measured by several groups Cao et al. (2003); Chou, Cho, Lee, Abel, Matan & Lee (2004); Jin et al. (2005); Lorenz et al. (2004); Oeschler et al. (2005); Ueland et al. (2004); Yang et al. (2005). The specific heat jump at superconducting transition temperature ΔC/γT c is estimated to be approximately 0.7, which is half of the BCS value 1.43. The small jump suggests either the quality of the sample is insufficient, or the superconductivity is an unconventional type with nodes. Below the superconducting transition temperature, C/T does not follow exponential temperature dependence but follows power law behavior, which is universally observed in unconventional superconductor. The power law behavior observed from nuclear-spin-lattice relaxation rate 1/T 1 measurement also supports unconventional superconductivity Fujimoto et al. (2004); Ishida et al. (2003). The results of 1/T 1 measurements are presented in § 4. The values of Sommerfeld constant, which are 12 ∼ 16 mJ/molK 2 depending on samples, are comparable to those of anhydrous compound Na 0.3 CoO 2 and less than those of mother compound Na 0.7 CoO 2 . It is curious that the BLH compound which has smaller density of state compared to mother compounds demonstrates superconductivity, while a single crystal of Na 0.7 CoO 2 with larger density of state is not a superconductor. The hydrous phases ought to have specific mechanisms to induce superconducting pairs. The discovery of magnetism in a sufficiently water intercalated BLH compound provides important information to understand the origin of superconductivity. The superconducting BLH is located in the close vicinity of magnetic phase, as in the case for heavy Fermion superconductors. This similarity lets us invoke that the magnetic fluctuations near magnetic criticality can induce superconductivity in BLH system. The magnetic fluctuations are examined in detail with nuclear quadrupole resonance and nuclear magnetic resonance technique in order to unravel the superconducting mechanisms. 17 Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 . yH 2 O 4 Will-be-set-by-IN-TECH 3. Nuclear magnetic resonance and nuclear quadrupole resonance 3.1 Nuclear quadrupole resonance measurement In this section, the fundamental principles of nuclear quadrupole resonance (NQR) are briefly reviewed. Resonance phenomena are observed between split nuclear states and radio frequency fields with energy comparable to the splitting width. To observe the resonance, degenerated nuclear spin states have to be split by a magnetic field and/or an electric-field gradient (EFG). For NQR measurements, a magnetic field is not required because the nuclear levels are split only by the electric-field gradient. Under zero magnetic field, nuclear levels are determined by the electric quadrupole Hamiltonian H Q , which describes the interaction between the electric quadrupole moment of the nuclei Q and the EFG at the nuclear site. In general, H Q is expressed as H Q = ν zz 6  (3I 2 z −I 2 )+ 1 2 η (I 2 + + I 2 − )  ,  ν zz = 6e 2 qQ 4I(2I −1)  (1) where eq (= V zz ) and η =(V yy −V xx )/V zz are the EFG along the principal axis (z axis) and the asymmetry parameter, respectively. The resonant frequency is calculated by solving the Hamiltonian. From the measurement of these resonant frequencies, ν zz and η are estimated separately. These two quantities provide information concerning with the Co-3d electronic state and the subtle crystal distortions around the Co site, because the EFG at the Co site is determined by on-site 3 d electrons and ionic charges surrounding the Co site. T he ionic charge contribution is estimated from a calculation, in which the ions are assumed to be point charges (point-charge calculation). The result of the point-charge calculation indicates that V zz is mainly dependent on the thickness of the CoO 2 layers, because the effect of the neighboring O 2− ions is larger than that of oxonium ions and Na + ions that are distant from the Co ions. Due to the ionic charge contribution, the resonant frequency was found to increase with the compression of the CoO 2 layers. When small magnetic fields, which are comparable to EFG, are applied, the perturbation method is no longer valid to estimate the energy level. The resonant frequency should be computed numerically by diagonalizing Hamiltonian, which includes both Zeeman and electric quadrupole interactions. The total Hamiltonian is expressed as H = H Q + H Z (2) = ν zz 6  (3I 2 z −I 2 )+ 1 2 η (I 2 + + I 2 − )  −γ¯h  I z H z + I x H x + I y H y  .(3) The results of a numerical calculation is displayed in Fig. 2, where the parameters ν zz , η are set to be 4.2 MHz and 0.2, respectively. The shift of the resonant frequency depends on the direction of the small magnetic fields. The magnetic fields parallel to the principal axis of EFG (z axis) affect the transition between the largest m states, while spectral shift of this transition is small when the magnetic fields are perpendicular to z axis. In other word, when internal magnetic fields appear in the magnetically ordered state, the direction of the internal fields can be determined from the observation of NQR spectrum with the highest resonant frequency above and below the magnetic transition. 3.2 Nuclear spin-lattice relaxation rate The nuclear spin system has weak thermal coupling with the electron system. Through the coupling, heat supplied to the nuclear spin system by radio-frequency pulses flows into the 18 Superconductivity – Theory and Applications Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 ·yH 2 O5 0.0 0.1 0.2 0 4 8 12 16 NQR Frequency ( MHz ) Magnetic Field ( T ) -1/2 1/2 1/2 3/2 3/2 5/2 5/2 7/2 + - + - + - + - + - + - Fig. 2. NQR frequency calculated from equation (3) with small magnetic fields up to 0.2 T. The solid and dashed lines are the resonant frequency in magnetic fields perpendicular and parallel to the principal axis of EFG (z axis). The parameters ν zz and η were set to the realistic values of 4.2 MHz and 0.2, respectively electron system, and the excited nuclear spin system relaxes after a characteristic time scale T 1 . The nuclear spin-lattice relaxation rate 1/T 1 contains important information concerning with the dynamics of the electrons at the Fermi surface. When the nuclear spin system is relaxed by the magnetic fields induced by electron spins δH, the transition probability is formulated by using the Fermi’s golden rule as W m,ν→m+1,ν  = 2π ¯h    m, ν|γ n ¯hI ·δH|m + 1, ν      2 δ(E m + E ν −E m+1 − E ν  ).(4) With this transition probability, 1/T 1 is defined as 1 T 1 = ∑ ν,ν  2W m,ν→m+1,ν  (I −m)(I + m + 1) (5) = γ 2 n 2  ∞ −∞ dt cos ω 0 t  δH + (t)δH − (0)+δH − (t)δH + (0) 2  .(6) Equation (6) is derived by expanding equation (4) with the relation δH + (T)= exp(iHt/¯h)δH + exp(−iHt/¯h) . When fluctuation-dissipation theorem is adopted to equation (6), the general representation for 1/T 1 is obtained. 1 T 1 = 2γ 2 n k B T (γ e ¯h) 2 ∑ q A q A −q χ  ⊥ (q, ω 0 ) ω 0 .(7) Here, A q and χ  ⊥ (q, ω) are the coupling constant in q space and the imaginary part of the dynamical susceptibility, respectively. ω 0 in the equation is the NM R frequency, which is usually less than a few hundreds MHz. The q dependence of A q is weak, when 1/T 1 is measured at the site where electronic spins are located. 19 Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 . yH 2 O 6 Will-be-set-by-IN-TECH The temperature dependence of 1/T 1 has been studied by using the self-consistent renormalization (SCR) theory Moriya (1991). The dynamical susceptibility assumed in this theory is formulated as χ (Q + q, ω)= χ(Q) 1 + q 2 A χ(Q) − iωq −θ Cχ(Q) .(8) The dynamical susceptibility is expanded in q space around Q, which represents the ordering wave vector. When the magnetic ordering is ferromagnetic (Q = 0), θ = 1 is used to calculate χ (q, ω), and when it is anti-ferromagnetic (Q > 0), θ is zero. The parameters A and C are determined self-consistently to minimize the free energy. The SCR theory is available when the electronic system is close to a magnetic instability. The temperature dependence of 1/T 1 above T C and T N is derived using the renormalized dynamical susceptibility. The results depend on the dimensionality and the θ values, which determine that the magnetic ordering is ferromagnetic (FM) or anti-ferromagnetic (AFM). The temperature dependence anticipated from the SC R theory is listed in Table 1. 2-D 3-D FM 1/T 1 ∝ T/(T − T C ) 3/2 1/T 1 ∝ T/(T −T C ) AFM 1/T 1 ∝ T/(T − T N ) 1/T 1 ∝ T/(T −T N ) 1/2 Table 1. Temperature dependence of 1/T 1 anticipated from the SCR theory. In the superconducting state, thermally exited quasiparticles can contribute to the Knight shift K and the nuclear spin-lattice relaxation rate 1/T 1 . Since the quasiparticles do not exist within the superconducting gap, the energy spectrum of the quasiparticle density of state is expressed as N (E; θ, φ)= N 0 E  E 2 −Δ 2 (θ, φ) for E > Δ(θ, φ) (9) = 0for0< E < Δ(θ, φ), (10) where E is the quasiparticle energy, which is determined as E 2 = ε 2 + Δ 2 ,andN 0 is the density of state in the normal state. In order to obtain the total density of state N (E), N(E; θ, φ) should be integrated over all the solid angles. N(E) is calculated with considering simple angle dependence for Δ, and the resulting energy spectra are represented in Fig. 3. The angle dependence of the superconducting gap, which we considered for the calculations, are listed below. Δ (θ, φ)=Δ 0 for s-wave, (11) Δ (θ, φ)=Δ 0 sin θe iφ for p-wave axial state, (12) Δ (θ, φ)=Δ 0 cos θe iφ for p-wave polar state, (13) Δ (θ, φ)=Δ 0 cos 2φ for two-dimensional d-wave. (14) The temperature dependence of the Knight shift and the nuclear spin-lattice relaxation rate in the superconducting state can be computed from the following equations wit h using N (E) 20 Superconductivity – Theory and Applications Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 ·yH 2 O7 calculated above. The temperature dependence of the gap maximum Δ 0 was assumed to be that anticipated from the BCS theory for all the gap symmetry considered above. K = A hf Nμ B χ s = − 4μ B A hf N  N(E) ∂ f (E) ∂E dE, (15) 1 T 1 = πA 2 hf ¯hN 2   1 + Δ 2 0 E 2  N (E) 2 f (E)(1 − f (E))dE. (16) Here, f (E) is the Fermi distribution function. The term (1 + Δ 2 0 /E 2 ) in equation (16) is referred to as the coherence factor, which is derived from the spin flip process of unpaired electrons through the interactions between the unpaired electrons and the Cooper pairs Hebel & Slichter (1959). As an initial state |i, it is assumed that one unpaired electron with up spin and one Cooper pair have wave numbers k and k  , respectively. After the interaction between these particles, the wave numbers are exchanged, and the electronic spin of the unpaired electron can flip with preserving energy. The final state |f  is chosen to be one electron with down spin and wave number −k  , and one Cooper pair with wave number k. This process can contribute to the relaxation rate by exchanging the electronic spins and the nuclear spins. The initial state and the final state are expressed with using the creation and annihilation operators c ∗ k and c k 0.0 0.5 1.0 1.5 2.0 2.5 0 1 2 3 4 s wave- p wave axial- p wave polar- D2- d wave- u  OlGPVu W lGVΔ Fig. 3. Quasiparticle density of state in various superconducting states. Finite N s (E) e xists at the energy lower than maximum gap size, when superconducting gap has nodes. The energy dependence of N s (E) at low energy determines the exponents f or the power-law temperature dependence of physical quantities. 21 Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 . yH 2 O 8 Will-be-set-by-IN-TECH as |i =   1 −h k  +  h k c ∗ k  ↑ c ∗ − k  ↓  c ∗ k↑ |ψ 0  (17) |f  =   1 −h k +  h k c ∗ k↑ c ∗ − k↓  c ∗ − k  ↓ |ψ 0 , (18) where ψ 0 represents the vacuum s tate, and h k is determined as h k =(1 − ε k /E k )/2. The perturbation Hamiltonian, which flips one electronic spin, is described as H p = A ∑ k,k  1 2  I + c ∗ k  ↓ c k↑ + I − c ∗ k  ↑ c k↓  . (19) The transition probability from |i to |f  originating from H p is derived as    f |H p |i    2 = 1 2   1 −h k  1 −h k  +  h k  h k   2 (20) = 1 2  1 + ε k ε k  E k E k  + Δ 2 E k E k   . (21) Here, the anticommutation relation of c ∗ k and E k =  ε 2 k + Δ 2 are used. The second term of equation (21) is canceled out when this term is integrated over the Fermi surface, because ε k is the energy from the Fermi energy. The counter process that a down s pin flips to an up spin should also be considered. When this process is included, the transition probability becomes twice of |f |H p |i| 2 .ThethirdtermΔ 2 /E k E k  possesses finite value only for an s-wave superconductor w ith an isotropic superconducting gap, such as Al metal Hebel & Slichter (1959). This term vanishes when the superconducting pairing symmetry is p-wave and two-dimensional d-wave type, which are represented in equations (12), (13) and (14). In unconventional superconductors with an anisotropic order parameter, the temperature dependence of 1/T 1 shows power-law behavior, because the quasiparticle density of states exist even below the maximum value of the gap Δ 0 . The existence of the density of states in the small energy region originates from the nodes on the superconducting gap. In the p-wave axial state, where the superconducting gap possesses point nodes at θ = 0, π, N(E) is proportional to E 2 near E = 0. As a r esult, 1/T 1 is proportional to T 5 far below T c .Inthe p-wave polar state and the d-wave state, where the superconducting gap possesses line nodes at θ = π/2 and φ = 0, π/2, respectively, the temperature dependence of 1/ T 1 becomes T 3 , which is derived from the linear energy dependence of N (E) in the low energy region. The observation of the power-law behavior in the temperature dependence of 1/T 1 far below T c is strong evidence for the presence of nodes on the superconducting gap, and therefore, for the unconventional superconductivity. 4. Ground states of Na x (H 3 O) z CoO 2 ·yH 2 O 4.1 Superconductivity In order to investigate the symmetry of superconducting order parameter, 1/T 1 was measured at zero field using NQR signal of the best s uperconducting sample with T c = 4.7 K. The temperature dependence of 1/T 1 observed in the superconducting state shows a power-law behavior as shown in Fig. 4 Ishida et al. (2003). This power-law d ecrease starts just below T c without any increase due to Hebel-Slichter mechanism, and gradually changes the exponent 22 Superconductivity – Theory and Applications Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 ·yH 2 O9 from ∼ 3athalfofT c to unity below 1 K. The overall temperature dependence can be sufficiently fitted by the theoretical curve assuming the two-dimensional d-wave pairing state with the gap size 2Δ/ k B T c = 3.5 and residual density of state N res /N 0 ∼ 0.32. The unconventional superconductivity with nodes on the superconducting gap is concluded for the superconductivity in BLH compounds. The residual density o f states are generated by tiny amount of impurities inherent in the powder samples, because superconducting gap diminishes to zero along certain directions in the unconventional superconductors. Next, the normal-state temperature dependence of 1/T 1 T for BLH compound is compared with those of non-superconducting MLH and anhydrous compounds in order to identify the origin of superconductivity. Surprisingly, 1/T 1 T in MLH is nearly identical to that in anhydrous cobaltate, even though the water molecule content i s considerably different. In these compositions, gradual decrease in 1/T 1 T from ro om temperature terminates around 100 K, below which Fermi-liquid like Korringa behavior is observed. This gradual decrease in 1/T 1 T at high temperatures is reminiscent of the spin-gap formation in cuprate Alloul et al. (1989); Takigawa et al. (1989). The temperature dependence of the MLH and anhydrous samples are mimicked by  1 T 1 T  PG = 8.75 + 15 exp  − Δ T  (sec −1 K −1 ) (22) with Δ = 250 K. The value of Δ is in good agreement with the pseudogap energy ∼ 20 meV determined by photoemission spectroscopy Shimojima et al. (2006). The spin-gap behavior observed by relaxation rate measurement indicates the decrease in density of states due to the strong correlations. 1 10 100 0 10 20 T c Bilayer hydrate Monolayer hydrate unhydrous Na 0.35 CoO 2 1 / T 1 T ( s -1 K -1 ) T ( K ) (b) 0.1 1 10 100 0.1 1 10 100 1000 ~ T ~ T 3 1/T 1 ( s -1 ) T ( K ) T c = 4.7 K Superconducting Na x (H 3 O) z CoO 2 - yH 2 O (a) Fig. 4. (a) Temperature dependence of 1/T 1 measuredatzeromagneticfieldIshidaetal. (2003). Red solid curve is a theoretical fit to the date below T c = 4.7 K, for which line nodes on the superconducting gap are taken into account. (b) Te mperature dependence of 1/T 1 T in superconducting BLH compound, MLH compound, and anhydrous cobaltate Na 0.35 CoO 2 . The experimental data of the anhydrous cobaltate was reported by Ning et al. (2004). The dashed line represents the sample-independent pseudogap contribution, which is expressed in equation (22). Ihara et al. (2006) 23 Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound Na x (H 3 O) z CoO 2 . yH 2 O [...]... Takayama-Muromashi, E (20 03) Unconventional superconductivity and nearly ferromagnetic spin fluctuations in nax coo2 · yh2 o, J Phys Soc Jpn 72: 3041 Jin, R., Sales, B C., Khalifah, P & Mandrus, D (20 03) Observation of bulk superconductivity in nax coo2 · yh2 o and nax coo2 · yd2 o powder and single crystals, Phys Rev Lett 91: 21 7001 Jin, R., Sales, B C., Li, S & Mandrus, D (20 05) Dependence of the... (Ashcroft, 20 00; Babaev, 20 02; Babaev et al, 20 04) Recent discovery of high-temperature superconductivity in iron-based compounds (Kamihara et al., 20 08) have expanded a range of multiband superconductors Various thermodynamic and transport properties of MgB2 and iron-based superconductors were studied in the framework of two-band BCS model (Golubov et al., 20 02; Brinkman et al., 20 02; Mazin et al., 20 02; ... Tc and magnetic transition temperature TM of various samples reported in the literature Badica et al (20 06); Barnes et al (20 05); Cao et al (20 03); Chen et al (20 04); Chou, Cho, Lee, Abel, Matan & Lee (20 04); Foo et al (20 05; 20 03); Ihara et al (20 06); Jin et al (20 03; 20 05); Jorgensen et al (20 03); Lorenz et al (20 04); Lynn et al (20 03); Milne et al (20 04); Ohta et al (20 05); Poltavets et al (20 06);... Takayama-Muromachi, E (20 05) Phase diaram of superconducting nax coo2 · yh2 o, J Phys Soc Jpn 74: 29 09 Sakurai, H., Takda, K., Yoshii, S., Sasaki, T., Kindo, K & Takayama-Muromachi, E (20 03) Unconventional upper- and lower-crytical fields and normal-state magnetic susceptibility of the superconducting compound na0.35 coo2 · 1.3h2 o, Phys Rev B 68: 1 325 07 36 22 Superconductivity – Theory and Applications Will-be-set-by-IN-TECH... −1 20 SC 19.691 12. 39 4.8 – IM 19.739 12. 50 4.4 – 4 20 M1 19. 820 12. 69 3.6 6 6 20 M2 19.751 12. 54 – 5 5 20 Table 2 Various parameters for the samples shown in Fig 6 The θ and a values are determined from the fitting (see text) Figure 7(b) shows the temperature dependence of 1/T1 T in SC, IM, M1, and M2 samples The microscopic and macroscopic sample properties of these samples are summarized in Table 2. .. al., 20 02; Miranovic et al., 20 03; Dahm & Schopohl, 20 04; Dahm et al., 20 04; Gurevich, 20 03; Golubov & Koshelev, 20 03) Ginzburg-Landau functional for two-gap superconductors was derived within the weak-coupling BCS theory in dirty (Koshelev & Golubov, 20 03) and clean (Zhitomirsky & Dao, 20 04) superconductors Within the Ginzurg-Landau scheme the magnetic properties (Askerzade, 20 03a; Askerzade, 20 03b;... Unconventional Superconductivity Realized Near Magnetism in Hydrous Compound NaCompoundzNa x (H3 O) CoO22OH2 O Unconventional Superconductivity Realized Near Magnetism in Hydrous x(H3O) CoO2 z yH · y 35 21 superconductivity in nax coo2 · yh2 o – 59 co nmr studies, J Phys.:Condens Matter 18: 669–6 82 Knebel, G., Aoki, D., Braithwaite, D., Salce, B & Flouquet, J (20 06) Coexistence of antiferromagnetismn and superconductivity. .. properties of two-band superconductors The real boom in investigation of multi-gap superconductivity started after the discovery of two gaps in MgB2 (Nagamatsu et al., 20 01) by the scanning tunneling (Giubileo et al., 20 01; Iavarone et al., 20 02 ) and point contact spectroscopy (Szabo et al., 20 01; Schmidt et al., 20 01; Yanson & Naidyuk, 20 04) The structure of MgB2 and the Fermi surface of MgB2 calculated... M & Xu, Z (20 03) Superconductivity in a layered cobalt oxyhydrate na0.31 coo2 · 1.3h2 o, J Phys Condens Matter 15: L519 Chen, D P., Chen, H C., Maljuk, A., Kulakov, A., Zhang, H., Lemmens, P & Lin, C T (20 04) Single-crystal growth and investigation of nax coo2 and nax coo2 · yh2 o, Phys Rev B 70: 024 506 Chou, F C., Cho, J H., Lee, P A., Abel, E T., Matan, K & Lee, Y S (20 04) Thermodynamic and transport... spin relaxation in normal and superconducting aluminum, Phys Rev 113: 1504 Higemoto, W., Ohishi, K., Koda, A., Kadono, R., Sakurai, H., Takada, K., Takayama-Muromachi, E & Sasaki, T (20 06) Possible unconventional 34 20 Superconductivity – Theory and Applications Will-be-set-by-IN-TECH superconductivity and weak magnetism in nax coo2 · yh2 o probed by μsr, Physica B 374-375: 27 4 Higemoto, W., Ohishi, . ) Magnetic Field ( T ) -1 /2 1 /2 1 /2 3 /2 3 /2 5 /2 5 /2 7 /2 + - + - + - + - + - + - Fig. 2. NQR frequency calculated from equation (3) with small magnetic fields up to 0 .2 T. The solid and dashed lines are. & Lee (20 04); Foo et al. (20 05; 20 03); Ihara et al. (20 06); Jin et al. (20 03; 20 05); Jorgensen et al. (20 03); Lorenz et al. (20 04); Lynn et al. (20 03); Milne et al. (20 04); Ohta et al. (20 05);. et al. (20 06); Barnes et al. (20 05); Cao et al. (20 03); Chen et al. (20 04); Chou, Cho, Lee, Abel, Matan & Lee (20 04); Foo et al. (20 05; 20 03); Ihara et al. (20 06); Jin et al. (20 03; 20 05);