Nonlinear σ model for odd-frequency triplet superconductivity in superconductor/ferromagnet structures

We consider some properties of odd frequency triplet superconducting condensates. In order to describe fluctuations we construct a supermatrix sigma-model for the superconductor/ferromagnet or superconductor/normal-metal structures. We show that an odd frequency triplet superconductor, when in isolation or coupled to a normal metal, generally displays behaviour comparable to a superconductor with the usual singlet pairings. However, for spin dependent systems such as the superconductor/ferromagnet the two types of superconductor have quite different behaviour. We discuss this difference by considering transformations under which the sigma-model is invariant. Finally, we calculate the low energy density of states in a ferromagnet coupled to a singlet superconductor. If odd frequency triplet components are induced in the ferromagnet the density of states will have a micro-gap similar to the micro-gap found in normal metals coupled to a superconductor.