Ginzburg-Landau Analysis of the Critical Temperature and the Upper Critical Field for Three-Band Superconductors

Abstract

Using the microscopic formalism of Eilenberger equations, a three-band Ginzburg-Landau theory for the intraband dirty limit and clean interband scattering case is derived. Within the framework of this three-band Ginzburg-Landau theory, expressions for the critical temperature T c and the temperature dependence of the upper critical field 2 c H are obtained. Based on some special cases of the matrix of interaction constants, we demonstrate the influence of the sign of the interband interaction on the critical temperature and the upper critical field as compared with a two-band superconductor where it plays no role. We study also analytically and numerically the effect of its magnitude.

Effects of Pair-Hopping Coupling on Properties of Multi-Band Iron-Based Superconductors

“…Similar deflection of the gap from the BCS-like shape has been observed experimentally for, e.g., 111 [51], 122 [52], and 1111 [53] families of the iron-based superconductors (in a more realistic three band model, there is the pair of leading bands with similar but unresolved gaps coupled by spin fluctuations and the weakly coupled third band [54,55]) as well as in other multi-band superconductors such as PuCoGa 5 [56], (Li 1−x Fe x )OHFeSe [57], LnOFeAs [58], Sn(Pb)Mo 6 S 8 [59], or classical two-band MgB 2 [60][61][62][63]. In a case of MgB 2 one has detected also a similar character of the interplay between intra-and inter-band quantities, which has been observed in a temperature dependence of the critical Josephson currents from one band to the other of the MgB 2 -insulator-MgB 2 tunnel junctions [61,64], or in a more general case of the two-band Josephson junction [65].…”

Proximity and Josephson effects in microstructures based on multiband superconductors (Review Article)

“…A three-band superconductor in the clean limit and also in the current-free state can be described by the following Ginzburg-Landau functional 167,[172][173][174][175][176][177] F ¼ ð a 1 jw 1 j 2 þ a 2 jw 2 j 2 þ a 3 jw 3 j 2 þ 1 2 b 1 jw 1 j 4 þ 1 2 b 2 jw 2 j 4 þ 1 2 b 3 jw 3 j 4 þ K 1i jPw 1 j 2 þ K 2i jPw 2 j 2 þK 3i jPw 3 j 2 Àc 12 w à 1 w 2 þ w à 2 w 1 À Á…”

Upper Critical Field as a Probe for Multiband Superconductivity in Bulk and Interfacial STO

“…These give an accurate description of the physics when disorder scattering is strong, such that anisotropies of the Fermi surface are averaged out. We solve the multiband Usadel equations [8,33] in the limit where the gaps ∆ are very small. This describes the region very close to the transition from superconductor to normal metal and the Usadel equations may be linearised, simplifying their solution.…”