Surface critical magnetic field H<Subscript>c3</Subscript>(T) of a bulk superconductor MgB<Subscript>2</Subscript> using two-band Ginzburg-Landau theory

Two-band Ginzburg-Landau (TB G–L) equations for a bulk MgB₂ were solved analytically to determine the temperature dependence of surface critical magnetic fieldH _c3 (T). It is shown thatH _c3 (T) has the same temperature dependence with H_c2 (T), similar to the case of a single-band superconductor,H _c3 (T) = 166H _c2 (T). We use an elimination procedure for the decoupling of G–L equations of two-band superconductivity, which eases the calculations. It is expected that the temperature dependence forH _c3 (T) gives positive curvature nearT _c .     

Anisotropy of the upper critical field in MgB2: the two-gap Ginzburg-Landau theory

The upper critical field in MgB2 is investigated in the framework of the two-gap Ginzburg-Landau theory. A variational solution of linearized Ginzburg-Landau equations agrees well with the Landau level expansion and demonstrates that spatial distributions of the gap functions are different in the two bands and change with temperature. The temperature variation of the ratio of two gaps is responsible for the upward temperature dependence of in-plane Hc2 as well as for the deviation of its out-of-plane behavior from the standard angular dependence. The hexagonal in-plane modulations of Hc2 can change sign with decreasing temperature.     

Electron transport,penetration depth,and the upper critical magnetic field in ZrB<Subscript>12</Subscript> and MgB<Subscript>2</Subscript>

We report on the synthesis and measurements of the temperature dependences of the resistivity ρ, the penetration depth λ, and the upper critical magnetic field H_c2, for polycrystalline samples of dodecaboride ZrB₁₂ and diboride MgB₂. We conclude that ZrB₁₂ behaves as a simple metal in the normal state with the usual Bloch-Grüneisen temperature dependence of ρ(T) and with a rather low resistive Debye temperature T_R = 280 K (to be compared to T_R = 900 K for MgB₂). The ρ(T) and λ(T) dependences for these samples reveal a superconducting transition in ZrB₁₂ at T_c = 6.0 K. Although a clear exponential λ(T) dependence in MgB₂ thin films and ceramic pellets was observed at low temperatures, this dependence was almost linear for ZrB₁₂ below T_c/2. These features indicate an s-wave pairing state in MgB₂, whereas a d-wave pairing state is possible in ZrB₁₂. In disagreement with conventional theories, we found a linear temperature dependence, of H_c2(T) for ZrB₁₂ (H_c2(0) = 0.15 T).     

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。     

Dependence of the upper critical field on the defect concentration in MgB<Subscript>2</Subscript> and the electronic structure parameters

The upper critical field H _c 2 (H ‖ c) of the two-band superconductor MgB₂ is studied as a function of the residual resistivity ρ_n. It is found that the superconductor follows the standard trend: the slope-dH_c2/dT of the temperature dependence of H_c2(T) increases with the number of defects. The upper critical field in the clean limit is found, and direct estimations of the parameters of carriers in the 2D σ band (including the Fermi velocity and the coherence length) are made. The contribution of the electron scattering to the magnitude of H_c2 is determined, and the mean free path of electrons in samples with various defect concentrations is estimated. The density of states of σ electrons at the Fermi level is calculated using the dependence of the slope-dH_c2/dT on ρ_n and a band structure model. It is impossible to estimate this density of states directly, because the upper critical field is determined by the carriers of one band, whereas the resistivity depends on the carriers in both bands.     

Nonstoichiometry and critical temperature of MgB<Subscript>2</Subscript>

The influence of nonstoichiometry of the new high-temperature superconductor MgB₂ on its critical temperature was studied by the direct magnetooptical observations of the penetration and trapping of magnetic flux. To preclude the possible influence of accidental factors, a special sample with transition from pure boron to the MgB₂ with an excess of Mg was synthesized. In a narrow region near the unreacted boron, the magnetic-field trapping and screening disappear at a temperature 1.5 K higher than in the dominant stoichiometric region of the sample.     

Superconductivity in two-band systems with a variable carrier density: The case of MgB<Subscript>2</Subscript>

A theory of the thermodynamic properties of a two-band superconductor with a low carrier density is developed; it is based on a phonon superconductivity mechanism with a strong electron-phonon coupling. This theory can describe the variation of the critical temperature T _c, the energy gaps Δ₁ and Δ₂, and the relative electronic specific heat jump (C _S ? C _N)/C _N at T = T _c with the carrier density in the compound MgB₂ when substitutional impurities of various valences are introduced into this system. The values of T _c, Δ₁, and Δ₂ are shown to decrease as this compound is doped by electrons and to remain constant (or almost constant) as it is doped by holes. This behavior follows from the mechanism of filling the σ and π energy bands, which overlap at the Fermi surface. The theory agrees qualitatively with experimental data. This agreement is found to be better when intra-and interband electron scattering by an impurity potential is taken into account.     

Temperature dependence of the anisotropy parameter of the LiFeAs upper critical field in the two-band Ginzburg-Landau theory

An analytical formula is obtained for the temperature dependence of the anisotropy parameter of the upper critical field of a two-band superconductor in the context of the generalized Ginzburg-Landau theory for layered superconductors. The theoretical results are compared with the experimental data for new superconductor LiFeAs.     

用两带Ginzburg-Landau理论分析两带超导体Lu2Fe3Si5的表面临界磁场

用两带Ginzburg-Landau(GL)理论分析了Lu₂Fe₃Si₅的表面临界磁场,当超导体的表面与任一主晶面重合,且外磁场平行于超导体的表面时,比值H_c3/H_c2(H_C2是Lu₂Fe₃Si₅的上临界磁场)强烈依赖于温度. 当超导体的表面是bc平面,且 关键词： 两带超导体 GL理论 2Fe₃Si₅')" href="#">Lu₂Fe₃Si₅ 表面临界磁场     

Two regimes in the magnetic field response of superconducting MgB<Subscript>2</Subscript>

Using Scanning Tunneling Microscope at low temperature we explore the superconducting phase diagram in the π-band of the two-band superconductor MgB₂. In this band the peculiar shape of the local tunneling spectra and their dynamics in the magnetic field reveal the complex character of the quasiparticle density of states (DOS). The gap in the DOS is first rapidly filled with states in raising the magnetic field up to 0.5 T and then slowly approaches the normal state value: the gap is observed up to 2 T. Such a change in the DOS dynamics suggests the existence of two terms in the DOS of the π-band: a first one, reflecting an intrinsic superconductivity in the band and a second one, originating from an inter-band coupling to the σ-band. Our findings allow a deeper understanding of the unique phase diagram of MgB₂.     

X-ray photoemission study of MgB<Subscript>2</Subscript> films synthesized from in-situ annealed MgB<Subscript>2</Subscript>/Mg multilayers

Superconducting MgB₂ films were obtained by in-situ annealing of precursor multilayers deposited at low substrate temperature by sputtering from a MgB₂ stoichiometric target and by thermal evaporation of pure Mg. After an in-situ annealing at 500–600 °C, the films showed a zero resistance critical temperature up to 31 K. The as-obtained MgB₂ films were investigated by X-ray photoelectron spectroscopy (XPS) and X-ray auger electron spectroscopy (XAES). The electronic structure was studied by monitoring the B 1s, Mg 2p, O 1s core-levels and the Mg KL₂L₃ Auger line. For comparison, the electronic structure of an MgB₂ commercial superconducting sputtering target, of a not-annealed precursor film and of a sample obtained by direct sputtering from the MgB₂ target have also been investigated. Electron spectroscopy showed that in the superconducting systems the Mg KL₂L₃ Auger line kinetic energy position is always higher by about 0.9 eV with respect to the energy position of the same Auger line measured in the non-superconducting samples. PACS 74.25Jb; 74.78.Bz; 74.70.Ad     

Electron transport and anisotropy of the upper critical magnetic field in Ba<Subscript>0.68</Subscript>K<Subscript>0.32</Subscript>Fe<Subscript>2</Subscript>As<Subscript>2</Subscript> single crystals

Early work on the iron-arsenide compounds supported the view, that a reduced dimensionality might be a necessary prerequisite for high-T _c superconductivity. Later, however, it was found that the zero-temperature upper critical magnetic field, H _c2(0), for the 122 iron pnictides is in fact rather isotropic. Here, we report measurements of the temperature dependence of the electrical resistivity, ρ(T), in Ba_0.5K_0.5Fe₂As₂ and Ba_0.68K_0.32Fe₂As₂ single crystals in zero magnetic field and in Ba_0.68K_0.32Fe₂As₂ in static and pulsed magnetic fields up to 60 T. We find that the resistivity of both compounds in zero field is well described by an exponential term due to inter-sheet umklapp electron-phonon scattering between light electrons around the M point to heavy hole sheets at the Γ point in reciprocal space. From our data, we construct an H-T phase diagram for the inter-plane (H | c) and in-plane (H | ab) directions for Ba_0.68K_0.32Fe₂As₂. Contrary to published data for 122 underdoped FeAs compounds, we find that H _c2(T) is in fact anisotropic in optimally doped samples down to low temperatures. The anisotropy parameter, γ = H _c2 ^ab /H _c2 ^c , is about 2.2 at T _c . For both field orientations we find a concave curvature of the H _c2 lines with decreasing anisotropy and saturation towards lower temperature. Taking into account Pauli spin paramagnetism, we perfectly can describe H _c2 and its anisotropy.     

Low-temperature anomalies in MgB<Subscript>2</Subscript> thermal expansion

The thermal expansion coefficient α(T) of MgB₂ was measured at low temperatures both in a zero magnetic field and at H=36 kOe. As in the oxide HTSCs, a region of anomalous (negative) thermal expansion and a strong effect of magnetic field on α(T) were revealed. The results obtained indicate the anomalous properties of MgB₂ and the oxide HTSCs to follow a common pattern.     

Upper critical field <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>2</Subscript> in anisotropic superconductors with varying charge carrier density: Application of the theory to doped MgB<Subscript>2</Subscript>

A theory describing the magnetic properties of a two-band superconductor with a varying charge carrier density is constructed. The upper critical field H _c2^(ab) parallel to the ab plane and field H _c2^(c) parallel to the c axis are determined in the entire temperature range 0 < T < T _c . A considerable increase in upper critical field H _c2^(ab) as compared to H _c2^(c) because of strong anisotropy of the system is detected. Anisotropy of coefficient γ _H = H _c2^(ab) / H _c2^(c) is obtained as a function of temperature for pure MgB₂ and as a function of the chemical potential in the case when Mg and B atoms are replaced with other chemical elements. A correlation between the variation in the superconducting transition temperature upon an increase in the chemical potential and critical magnetic fields H _c2^(ab) and H _c2^(c) is observed. The effect of doping on magnetic anisotropy is also determined.     

Microwave surface resistance of pristine and neutron-irradiated MgB<Subscript>2</Subscript> samples in magnetic field

We report on the microwave surface resistance of two polycrystalline Mg¹¹ B₂ samples; one consists of pristine material, the other has been irradiated at very high neutron fluence. It has already been reported that in the strongly irradiated sample the two gaps merge into a single value. The mw surface resistance has been measured in the linear regime as a function of the temperature and the DC magnetic field, at increasing and decreasing fields. The results obtained in the strongly irradiated sample are quite well justified in the framework of a generalized Coffey and Clem model, in which we take into account the field distribution inside the sample due to the critical state. The results obtained in the pristine sample show several anomalies, especially at low temperatures, which cannot be justified in the framework of standard models for the fluxon dynamics. Only at temperatures near T_c and for magnetic fields greater than 0.5H_c2(T) the experimental data can quantitatively be accounted for by the Coffey and Clem model, provided that the upper-critical-field anisotropy is taken into due account.     

Physical property characterization of bulk MgB<Subscript>2</Subscript> superconductor

We report synthesis, structure/micro-structure, resistivity under magnetic field [ρ(T)H], Raman spectra, thermoelectric power S(T), thermal conductivity κ(T), and magnetization of ambient pressure argon annealed polycrystalline bulk samples of MgB₂, processed under identical conditions. The compound crystallizes in hexagonal structure with space group P6/mmm. Transmission electron microscopy (TEM) reveals electron micrographs showing various types of defect features along with the presence of 3–4 nm thick amorphous layers forming the grain boundaries of otherwise crystalline MgB₂. Raman spectra of the compound at room temperature exhibited characteristic phonon peak at 600 cm^-1. Superconductivity is observed at 37.2 K by magnetic susceptibility χ(T), resistivity ρ(T), thermoelectric power S(T), and thermal conductivity κ(T) measurements. The power law fitting of ρ(T) give rise to Debye temperature (Θ_D) at 1400 K which is found consistent with the theoretical fitting of S(T), exhibiting Θ _D of 1410 K and carrier density of 3.81 × 10²⁸/m³. Thermal conductivity κ(T) shows a jump at 38 K, i.e., at T_c, which was missing in some earlier reports. Critical current density (J_c) of up to 10⁵ A/cm² in 1–2 T (Tesla) fields at temperatures (T) of up to 10 K is seen from magnetization measurements. The irreversibility field, defined as the field related to merging of M(H) loops is found to be 78, 68 and 42 kOe at 4, 10 and 20 K respectively. The superconducting performance parameters viz. irreversibility field (H_irr) and critical current density J_c(H) of the studied MgB₂ are improved profoundly with addition of nano-SiC and nano-diamond. The physical property parameters measured for polycrystalline MgB₂ are compared with earlier reports and a consolidated insight of various physical properties is presented.     

Electron transport properties of MgB<Subscript>2</Subscript> in the normal state

We report measurements of the resistivity, ρ, and the Seebeck coefficient, S , of a MgB₂ sintered sample, and compare S with theoretical calculations based on precise electronic structure calculations. ρ is fitted well by a generalized Bloch-Grüneisen equation with a Debye temperature Θ _R of 1050 K. S is given by the sum of a diffusive and a phonon drag term and the behavior in the temperature region T _c < T < 0.1Θ _R follows the relationship AT+BT³. The phonon drag term indicates a strong electron-phonon interaction. The diffusive term, compared with calculations, suggests that σ bands give the main contribution to the Seebeck effect. Received 16 November 2001 and Received in final form 21 December 2001     

Ginzburg-landau slopes of the anisotropic upper critical magnetic field and band parameters in the superconductor (TMTSF)<Subscript>2</Subscript>ClO<Subscript>4</Subscript>

We theoretically determine the Ginzburg-Landau slopes of the anisotropic upper critical magnetic field in a quasi-one-dimensional superconductor and correct the previous works on this issue. By using the experimentally measured values of the Ginzburg-Landau slopes in the superconductor (TMTSF)ClO₄, we determine band parameters of its electron spectrum. Our main result is that the so-called quantum dimensional crossover has to happen in this material in magnetic fields, H = 3–8 T, which are much lower than the previously assumed. We discuss how this fact influences metallic and superconducting properties of the (TMTSF)₂ClO₄.     

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.