Derivation of the Ginzburg-Landau equations of a ferromagnetic p-wave superconductor

Abstract

We derive a Ginzburg-Landau free energy for a p-wave ferromagnetic superconductor. The starting point is a microscopic Hamiltonian including a spin generalised BCS term and a Heisenberg exchange term. We find that coexistence of magnetisation and superconductivity depends on the sign of the energy-gradient of the DOS at Fermi level. We also compute the tunneling contribution to the Ginzburg-Landau free energy, and find expressions for the spin-currents and Josephson currents across a tunneling junction separating two ferromagnetic p-wave superconductors.