Extended Ginzburg-Landau Formalism for Two-Band Superconductors

Abstract

Recent observation of unusual vortex patterns in MgB(2) single crystals raised speculations about possible "type-1.5" superconductivity in two-band materials, mixing the properties of both type-I and type-II superconductors. However, the strict application of the standard two-band Ginzburg-Landau (GL) theory results in simply proportional order parameters of the two bands-and does not support the "type-1.5" behavior. Here we derive the extended GL formalism (accounting all terms of the next order over the small τ=1-T/T(c) parameter) for a two-band clean s-wave superconductor and show that the two condensates generally have different spatial scales, with the difference disappearing only in the limit T→T(c). The extended version of the two-band GL formalism improves the validity of GL theory below T(c) and suggests revisiting the earlier calculations based on the standard model.

Finite temperature effective field theory and two-band superfluidity in Fermi gases

“…The extension of the EFT formulated in the above subsection to the two-band Fermi systems is particularly interesting due to recent intense discussions on the applicability of the GL approach to the coupled Fermi systems far below T c [17][18][19][20][21][22][23].…”

“…[13][14][15]), and lead to an intervortex interaction that can account for vortex clustering [16]. However, the validity of this simple extension has been the subject of intense debate [17][18][19][20][21][22][23]. Kogan and Schmalian [17,19] indicate that the two order parameters in a two-band superconductor should have the same length scale of spatial variation in the vicinity of the critical temperature T c , when T → T c .…”

“…In Refs. [20,21,24,25], an extended two-component GL formalism is found by performing an expansion of the free energy and the gap equation in powers of τ = 1 − T /T c to order τ 3/2 rather than τ 1/2 as is common for the standard GL formalism. This approach confirms the existence of two distinct length scales [26].…”

Simulation of the phase diagram of magnetic vortices in two-dimensional superconductors: evidence for vortex chain formation

“…Although large amount of experimental and theoretical efforts in this field has been made [10][11][12][13][14][15][16][17][18], the nature of the vortex clustering in multiband superconductors is still an intensely controversial issue now [17,[19][20][21][22]. In principle, the vortex cluster formation means that there might exist some type of attraction between vortices in addition to repulsion.…”

Beyond the standard model of Ginzburg–Landau theory: multiband superconductors

“…The presence of Josephson terms in multiband superconductors causes several problems in the Gor'kov type derivations. Recently in a series of papers Vagov and coworkers [12][13][14][15] have made detailed analysis and established a generalisation of the standard GL theory (which is correct to τ 1/2 ) by retaining additional terms in the expansion up to order τ (2n+1)/2 . In practice they have analysed the n = 1 corrections to the order parameter for 1, 2 and 3 bands .…”