The Role of Odd-Frequency Pairing in Multiband Superconductors

In this article we review recent progress in the understanding of multiband superconductivity and its relationship to odd-frequency pairing. We begin our discussion by reviewing the emergence of odd-frequency pairing in a simple two-band model, providing a brief pedagogical overview of the formalism. We then examine several examples of multiband superconducting systems in each case describing, both, the origin of the band degree of freedom and the nature of the odd-frequency pairing. Throughout, we attempt to convey a unified picture of how odd-frequency pairing emerges in these materials and propose that similar mechanisms are responsible for odd-frequency pairing in several analogous systems: layered two-dimensional heterostructures, double quantum dots, double nanowires, Josephson junctions, and systems described by isolated valleys in momentum space. We also review experimental probes of odd-frequency pairing in multiband systems, focusing on hybridization gaps in the electronic density of states, paramagnetic Meissner effect, and Kerr effect.