The Ginzburg-Landau expansion and the slope of the upper critical field in superconductors with anisotropic normal-impurity scattering

We carry out the Ginzburg-Landau expansion for superconductors with anisotropic s and d pairing in the presence of anisotropic normal-impurity scattering, which enhances the stability of d pairing with respect to disordering. We find that the slope of the curve of the upper critical field, |dH _c2/dT|_{T c}, in superconductors with d pairing behaves nonlinearly as disorder grows: at low scattering anisotropy the slope rapidly decreases with increasing impurity concentration, then gradually but nonlinearly increases with concentration, reaches its maximum, and then rapidly decreases, vanishing at the critical impurity concentration. In superconductors with anisotropic s pairing, |dH _c2/dT|_{T c} always increases with impurity concentration, finally reaching the familiar asymptotic value characteristic of the isotropic case, irrespective of whether there is anisotropic impurity scattering. Zh. éksp. Teor. Fiz. 112, 2124–2133 (December 1997)     

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.     

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.     

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.     

Theory of the upper critical field in layered superconductors with magnetic intercalates

We propose a model for the layered superconductors with electronically isolated magnetic intercalates in which the electrons propagate freely in the dirty superconducting layers with arbitrarily strong spin-orbit scattering, and spin-flip scatter off the magnetic ions during interlayer tunneling. We calculate the upper critical field H_c2 including demagnetization effects. In a parallel field below the dimensional-crossover temperature T¹, a new type of spin ordering is predicted.     

Quantum critical fluctuations in disordered d-wave superconductors

To explain the strong quasiparticle damping in the cuprates, Sachdev and collaborators proposed to couple the system to a critically fluctuating id(xy)- or is-order parameter mode. Here we generalize the approach to the presence of static disorder. In the id case, the order parameter dynamics becomes diffusive, but otherwise much of the phenomenology of the clean case remains intact. In contrast, the interplay of disorder and is-order parameter fluctuations leads to a secondary superconductor transition, with a critical temperature exponentially sensitive to the impurity concentration.     

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.     

Effect of ion irradiation on the upper critical magnetic field in electronic and hole d-wave superconductors

The effect of ion irradiation on the upper critical magnetic field H _c2 in electronic and hole high-temperature superconductors is studied. It is shown that the variation of H _c2 may be connected with the d-wave symmetry of the order parameter.     

The Ginzburg-Landau parameter in the case of non-pure superconductors

The concept of the Ginzburg-Landau parameter, κ, and of its extension to the case of non-pure materials is discussed in the framework of the BCS formulation and of the boson formulation. The data derived from several experiments performed on different samples containing various concentrations of scalar impurities are analyzed. We find that the value of κ for pure Ta, Nb and V is 0.350, 0.778 and 0.802, respectively. The theoretical dependence of κ by the electron mean free path is compared with the experimental behavior.     

Fermi surface topology and the upper critical field in two-band superconductors: application to MgB2

Recent measurements of the anisotropy of the upper critical field B(c2) on MgB2 single crystals have shown a puzzling strong temperature dependence. Here, we present a calculation of the upper critical field based on a detailed modeling of band structure calculations that takes into account both the unusual Fermi surface topology and the two gap nature of the superconducting order parameter. Our results show that the strong temperature dependence of the B(c2) anisotropy can be understood as an interplay of the dominating gap on the sigma band, which possesses a small c-axis component of the Fermi velocity, with the induced superconductivity on the pi-band possessing a large c-axis component of the Fermi velocity. We provide analytic formulas for the anisotropy ratio at T=0 and T=T(c) and quantitatively predict the distortion of the vortex lattice based on our calculations.     

Nonlinear critical slowing down of the one-component Ginzburg-Landau field

We discuss nonlinear relaxation processes of the one-component Ginzburg-Landau field that occur near the critical point after a sudden change in temperature or in the symmetry breaking field. A universal form of the equation of motion for the order parameter at the one-loop level is derived and integrated for several cases of interest. From the results some characteristic universal amplitude ratios can be extracted.     

Upper critical field in the heavy fermion superconductors

The upper critical field H_c2 (T) and its temperature derivative at T_c in the heavy fermion superconductors have been calculated by using the simplified Kondo lattice model.     

Anisotropy of the upper critical field in MgB<Subscript>2</Subscript>: The two-band Ginzburg-Landau theory

The temperature dependence of the anisotropy parameter of the upper critical field \(\gamma _{H_{c2} } (T) = H_{c2}^\parallel (T)/H_{c2}^ \bot (T)\) is calculated using the two-band Ginzburg-Landau theory for layered superconductors. It is shown that the anisotropy parameter γ(T) increases with decreasing temperature. The results of the calculations are in agreement with experimental data for single crystals of MgB₂ and with other calculations.     

Upper critical field of anisotropic superconductors

The upper critical field of anisotropic superconductors described by the effective mass model is calculated in the general direction of the applied magnetic field.     

The critical magnetic field of anisotropic two-band magnetic superconductors

The upper and lower critical fields, and the critical field ratio of an anisotropic two-band magnetic superconductor in the Ginzburg–Landau (GL) scenario is derived analytically. The temperature-dependent upper critical field is investigated and applied to Fe-based superconductors. We find that a very high value of zero-temperature upper critical field in Fe-based superconductors can be found in the negative differential susceptibility region. The temperature-dependent upper critical field is presented in two formulas, in the empirical view and in the GL two-band view, which agrees with the experimental results.