Analytic proposal for p + ip coupling in three-band Ginzburg-Landau model

Abstract

In this contribution, we propose a theoretical Josephson coupling for a superconducting system in the three-component time-dependent Ginzburg-Landau model. We study a system with three superconducting bands ψ 1, ψ 2, and ψ 3 in the superconducting condensate. The coupling between bands is of the form γ 12, γ 13 and γ 23, taking into account couplings of each of the bands with the other two. We show the mathematical development of the final form of the complete set of acopled non-linear time-dependent Ginzburg-Landau differential equations, considering the coupling between the three bands, also we show that this coupling imposes a phase difference between the different components of the superconducting order parameter.