Ginzburg-Landau equations for layered-wave superconductors

Based on Gor’kov’s theory of weakly coupled superconductors, the Ginzburg-Landau equations for layered (Formula presented)-wave superconductors are derived, the order parameter of which is assumed to belong to a nontrivial two-dimensional representation. This calculation allows us to microscopically determine the expansion coefficients of the Ginzburg-Landau free-energy functional with respect to the order parameter. The main feature of the vortex solution is briefly discussed. It is found that the extreme condition for the nonaxisymmetric singly quantized vortices is not ensured in the weak-coupling limit. If the discrete crystal symmetry is included, the axisymmetric singly quantized vortex is stable. In addition, the upper critical field is also solely determined within the weak-coupling framework.