Effective Ginzburg–Landau free energy functional for multi-band isotropic superconductors

Abstract

It has been shown that interband mixing of gradients of two order parameters (drag effect) in an isotropic bulk two-band superconductor plays important role -such a quantity of the intergradients coupling exists that the two-band superconductor is characterized with a single coherence length and a single Ginzburg-Landau (GL) parameter. Other quantities or neglecting of the drag effect lead to existence of two coherence lengths and dynamical instability due to violation of the phase relations between the order parameters. Thus so-called type-1.5 superconductors are impossible. An approximate method for solving of set of GL equations for a multi-band superconductor has been developed: using the result about the drag effect it has been shown that the free-energy functional for a multi-band superconductor can be reduced to the GL functional for an effective single-band superconductor.

Non-Adiabatic Effects in Superconducting Intermetallic Borocarbides

“…The evidence for a multi-band nature of the superconductivity in YNi 2 B 2 C and LuNi 2 B 2 C was reported among others in the papers [8,9]. One of the main features of these materials is the presence of two energy gaps which, however, vanish at the same critical temperature [10]. Our previous theoretical work on intermetallic borocarbides YPd 2 B 2 C, YPt 2 B 2 C and LaPt 2 B 2 C [11] shows that the experimental values of the critical temperature cannot be properly reproduced using the commonly accepted value of the Coulomb pseudopotential.…”

BCS theory with the external pair potential

“…In a case of the contact of two metal the critical temperature of the source drops, however in a case of the multi-band superconductor the proximity effect supports superconducting state in all bands. k B T c2 < 2∆ 1 k B T c1 as it can be in two-band superconductors [6,7]. The gap ∆3(T ) asymptotically aspires to zero as temperature rises, so that 2∆ 3 k B T c3 = 0.…”

“…-quasiaverages Bogolyubov method. In the other case the operator can have a U (1) × U (1) symmetrical form k υa + k↑ a + −k↓ + υ + a −k↓ a k↑ , where υ is the order parameter of another superconductor, for example, the boundary (proximity) effect, when a superconductor is placed in contact with a normal metal [3] or interband mixing of two order parameters belonging to different bands in a multi-band superconductor [5][6][7] occurs.…”

“…However the critical temperature can be enlarged by violation the ratio (1) as ∆/T c → 0 due to some addition influence on condensate of Cooper pairs as shown in Fig.(1). The simplest examples of such systems are systems where the proximity effect takes place: two superconductors are placed in contact [3], or in multi-band superconductors where the interband mixing of order parameters from different bands occurs [5,6]. In this cases the Cooper pairs are injected into the superconductor (band) from another superconductor (band) with higher critical temperature (stronger interaction) which plays a role of a source of Cooper pairs.…”

“…In this cases the Cooper pairs are injected into the superconductor (band) from another superconductor (band) with higher critical temperature (stronger interaction) which plays a role of a source of Cooper pairs. As a result in a band with lower critical temperature the ratio (1) can be violated as k B T c > ∆ [6,7] as illustrated in Fig.(1). However the source is function of temperature with own critical temperature.…”