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

TL;DR

This paper derives a Ginzburg-Landau free energy framework for ferromagnetic p-wave superconductors starting from a microscopic Hamiltonian, revealing conditions for coexistence of magnetization and superconductivity and analyzing tunneling phenomena.

Contribution

It introduces a novel Ginzburg-Landau model for ferromagnetic p-wave superconductors based on microscopic Hamiltonians, including tunneling and current calculations.

Findings

Coexistence depends on the sign of the energy-gradient of the DOS at Fermi level.

Derived expressions for spin-currents and Josephson currents across tunneling junctions.

Provided a microscopic foundation for phenomenological models of ferromagnetic p-wave superconductivity.

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.