Two-band calculations on the upper critical field of superconductor NbSe2

Based on two-band Ginzburg–Landau theory, we study the temperature dependence of upper critical field for superconducting crystal NbSe₂. The results reproduce the experimental data in a broad temperature range, especially the upward curvature near the transition temperature. Our calculations also indicate that in NbSe₂ the band with the smaller gap is almost isotropic, and most probably located on the bonding Nb Fermi sheets.     

Unusual upper critical field of the ferromagnetic superconductor UCoGe

We report upper critical field B(c2)(T) measurements on a single-crystalline sample of the ferromagnetic superconductor UCoGe. B(c2)(0) obtained for fields applied along the orthorhombic axes exceeds the Pauli limit for B parallela,b and shows a strong anisotropy B(c2)(a) approximately B(c2)(b)>B(c2)(c). This provides evidence for an equal-spin pairing state and a superconducting gap function of axial symmetry with point nodes along the c axis, which is also the direction of the uniaxial ferromagnetic moment m(0)=0.07micro(B). An unusual curvature or kink is observed in the temperature variation of B(c2) which possibly indicates UCoGe is a two-band ferromagnetic superconductor.     

二带超导体上临界磁场的各向异性

采用二带Ginziburg-Landau(G-L)理论模型计算了各向异性超导体的上临界磁场,发现上临界磁场Hc2的解析式中包含序参量的各向异性和有效质量的各向异性;上临界磁场ab-面内分量Hc|2|ab、c-轴方向分量Hc|2|ab与实验数据符合;上临界磁场比率在实验许可范围之内。     

Temperature dependence of the upper critical field of superconducting alloys

The upper critical field,H _c2, is calculated in the temperature range close toT _c for arbitrary values of the mean free path 1. The method is to treat the fourth-order term in the linearized differential equation for the gap parameter as a perturbation to the harmonic oscillator equation. The Nambu-Tuan term, which determines the structure of the “clean-limit” and “dirty-limit” parts of the fourth-order term, is calculated by means of the ladder diagram technique for impurity interaction lines. The result is that the magnitude of the slope of the curveH _c2/√2H _c κ versust=T/T _c att=1 decreases monotonically from the value 0.41 to 0.12 as the ratio of the BCS coherence lengthξ ₀ to the mean free path 1 increases from 0 to ∞. For 1?ξ ₀ this slope is about 0.26.     

Universal behavior of the upper critical field in iron-based superconductors

The newly discovered iron-based high temperature superconductors have demonstrated rich physical properties. Here we give a brief review on the recent studies of the upper critical field and its anisotropy in a few typical series of the iron-based superconductors (FeSCs). In spite of their characters of a layered crystal structure, all the FeSCs possess an extremely large upper critical field and a weak anisotropy of superconductivity, being unique among the layered superconductors. These particular properties indicate potential applications of the FeSCs in the future. Based on the experimental facts of the FeSCs, we will discuss the possible mechanisms of pair breaking in high magnetic fields and its restrictions on the theoretical analysis of the superconducting pairing mechanisms.     

The upper critical field in two-band layered superconductors

The upper critical field of clean MgB₂ is investigated using the two-band layered Ginzburg--Landau (GL) theory. The calculated results are fitted to the experimental data of clean MgB₂ crystal very well in a broad temperature range. Based on the GL theory for clean superconductors, a phenomenological theory for dirty superconductor is proposed. Selecting appropriate parameters, two-band layered GL theory is successfully applied to the crystal of Mg(B_1-xC_x)₂ and the neutron irradiation samples of MgB₂.     

Temperature dependence of the surface upper critical field of superconducting alloys

The temperature dependence of the surface upper critical field,H _c3, nearT _c is calculated for arbitrary values of the mean free pathl by taking into account the fourthorder term of the generalized Ginzburg-Landau theory. For finitel the boundary condition is modified such that the normal derivative of the energy gap at the surface becomes positive. The slope of the curveH _c3/H _c2 versust=T/T _c att=1 is found to decrease monotoneously from zero to ?1.040 as one goes from the “dirty” to the “clean” limit.     

Finite width effect on the upper critical field Hc2 of superconducting networks

A recent prediction for the continuum limit of the upper critical field of infinite superconducting networks H_c2(T)= dH^(bulk)_c2 (d=spatial dimension of the network) is checked experimentally. A direct comparison of the measured critical fields on both samples: film and infinite 2D regular networks, made of the same material, support strongly this theoretical prediction. The deviation of the proportionality coefficient from d=2 is attributed to the finite width of wires. Wires of finite width are shown to be responsible for a renormalization of the diffusion coefficient of Cooper pairs. The expression so obtained for H_c2 as a function of the filling factor is consistent with the measured value.     

Parallel upper critical field of niobium/graphite bilayers

The influence of the superconducting proximity effect to the upper critical field (H_C) in niobium/graphite bilayers was studied and related to the ratio : and are the transition temperature of Nb/KG film and that of Nb film respectively. The thickness of niobium (Nb) film was controlled about 40 nm, and that of graphite (kish graphite: KG) film ranged from 120 nm to 140 nm. For making a specimen, Nb was deposited on a KG film and a quartz glass substrate simultaneously, and magnetic field was applied parallel to the Nb/KG interface. H_C of Nb/KG film () lowered from that of Nb film () at all temperatures within this work, and the value of ΔH_C defined as showed different temperature dependence among samples, depending on whether < or 1.00. This behavior of H_C suggests the additional existence of the interference of electrons in the clean KG film.     

Thermal conductivity of superconducting lead-indium alloys near the upper critical field

The thermal conductivity of a series of lead/indium alloys was measured in the normal, superconducting and mixed states. The electronic part of the thermal conductivity near the upper critical field was compared with the theory of Caroli and Cyrot. There is good agreement in the dirty limit but large deviations are observed as the indium concentration is reduced.     

Quantum size effects on the perpendicular upper critical field in ultrathin lead films

We report the thickness-dependent (in terms of atomic layers) oscillation behavior of the perpendicular upper critical field Hc2perpendicular in the ultrathin lead films at the reduced temperature (t = T/Tc). Distinct oscillations of the normal-state resistivity as a function of film thickness have also been observed. Compared with the Tc oscillation, the Hc2perpendicular shows a considerable large oscillation amplitude and a pi phase shift. The oscillatory mean free path caused by the quantum size effect plays a role in Hc2perpendicular oscillation.     

超导材料NbS2上临界磁场的理论分析

根据两带Ginzburg-Landau 理论计算了层状超导材料NbS₂的上临界磁场, 以及上临界磁场各向异性参数随温度的变化情况, 并将NbS₂与MgB₂, NbSe₂上临界磁场的各向异性进行比较. 所得计算结果与已有实验数据符合得很好, 充分说明了NbS₂的超导电性具有两能隙特征. NbS₂上临界磁场各向异性参数在5.0 K附近逐渐变小, 这与MgB₂和NbSe₂有相似之处. 但NbS₂的上临界磁场各向异性参数大约为7.3, 明显大于MgB₂和NbSe₂. 计算结果还表明, NbS₂较大能隙所对应能带的有效质量比约为54, 另一能带的有效质量基本为各向同性.