Non-Abelian Ginzburg-Landau Theory of Spin Triplet Superconductivity

Abstract

We present an SU(2)xU(1) generalization of the Ginzburg-Landau theory of the spin triplet ferromagnetic superconductivity which could also describe the physics of the spin triplet magnon spintronics, where the SU(2) gauge interaction of the magnon plays the central role. The theory is made of the massive photon, massless neutral magnon, massive non-Abelian magnon, and the Higgs scalar field which represents the density of the Copper pair. It has the following characteristic features, the long range magnetic interaction mediated by the massless magnon, two types of conserved supercurrents (the ordinary charge current and the magnon spin current), and the non-Abelian Meissner effect generated by the spin current. It has two types of vortices, the quantized magnetic and spin vortices. Moreover, it has two types of monopoles, the monopole which has the ordinary magnetic charge and the one which has the spin magnetic charge. The theory is characterized by three scales. In addition to the correlation length fixed by the mass of the Higgs field it has two different mass scales, the one fixed by the mass of the photon and the other fixed by the mass of the off-diagonal magnon. We discuss the physical implications of the theory of the spin triplet superconductivity in condensed matter physics.