Hc2 of anisotropy two-band superconductors by Ginzburg–Landau approach

Abstract

The purpose of this research is to study the upper critical field (H c2 ) of two-band superconductors by two-band Ginzburg -Landau approach. The analytical formula of H c2 included anisotropy of order parameter and anisotropy of effective-mass are found . The parameters of the upper critical field in ab-plane( but it has an unusual temperature dependence. Askerzade [10] study H c1 (T) and H c2 (T) for MgB 2 and nonmagnetic borocarbides by using the isotropy two-band Ginzberg-Landau model. He shows the complicate formula of critical magnetic field. In the H c2 consideration, his formula is less fit to experimental data than Drechsler 's [11]. In the recent work of Dao and Zhitomirsky [12] ,they study the effect of angular and temperature on upper critical field of MgB 2 determined with the anisotropy two-band Ginzberg-Landau theory. They found that the temperature variation of the ratio of two gaps is responsible for the upward temperature dependence of in-plane H c2 as well as for the deviation of its out-of-plane behavior from the standard angular dependence.In this paper, we study the upper critical magnetic field( 2 c H ) of anisotropy two-band swave superconductors by Ginzburg-Landau theory . We can find the formula of H c2 included anisotropy of order parameter and anisotropy of effective-mass . The upper critical field in abplane( ab c

A review of two-band superconductivity: materials and effects on the thermodynamic and reversible mixed-state properties

“…Further properties derived from Ginzburg Landau theory are the upper and lower critical fields, the characteristic lengths, and the corresponding anisotropies as well as thermodynamic quantities [3,5,11,[13][14][15]. For example, it was demonstrated that a positive curvature of the upper critical field near the transition temperature may result from two-band superconductivity [3,5,13]. This would also result in a temperature dependent anisotropy, which could be quite different from that of the magnetic penetration depth [5].…”

The critical magnetic field of anisotropic two-band magnetic superconductors

“…The Helmholtz free energy of Ginzburg and Landau [1] theory can be modified to describe the critical magnetic field in non-magnetic superconductors and magnetic superconductors both in one-band and twoband presented in Refs. [1][2][3][4][5][6][7][8][9][10][26][27][28]. For isotropic two-band GL theory, there are two order parameters in the Ginzburg-Landau functional that free energy can be written down as…”

“…He showed the presence of two order parameters in the GL theory gave a non-linear temperature-dependence upper and lower critical magnetic field. Askerzade [7,8] , Udomsamuthirun et al [9],Minxia and Zi-Zhao [10] studied the upper critical field of anisotropic twoband superconductors by GL theory. The compact form of upper critical magnetic field of anisotropic two-band s-wave superconductor was found [9].…”

Angular dependence of upper critical field in two-band Ginzburg–Landau theory

“…For instance, the effect of positive curvature in H c2 is enhanced due to the inclusion of intergradient interaction term. In a very recent work [17] it is shown that this term is also important in the case of inclusion of anisotropic order parameters.…”

“…Theoretical calculations of angular dependence using quasi-classical Uzadel equations were performed by Golubov and Koshelev [24]. Anisotropy effects in the framework of above presented two-band GL theory [13] was calculated very recently by Udomsamuthirun et al [17]. However, in this work masses in different bands were taken to be the same and different character of effective masses in different bands was not taken into account.…”