Half quantum vortices and Majorana fermions in triplet superconductors

Half quantum vortices (HQVs) in superfluid $^3He-A$ have been speculated since 1976. Two years ago, Yamashita et al reported a very unusual NMR satellite in the rotating superfluid $^3He-A$ in a parallel plate geometry. Recently this satellite has been interpreted in terms of HQVs. Also, the strong flux pinnings in the triplet superconductors $UPt_3, Sr_2RuO_4$ and $U_{1-x}Th_xBe_{13}$ have been discovered by Mota and her colleagues which are interpreted in terms of HQVs. We shall first review the bound state spectra around a single vortex in unconventional superconductors, which provides the necessary background. In particular, we find the zero modes of the Majorana fermions in some of triplet superconductors $UPt_3, Sr_2RuO_4$ and $CePt_3Sn$. Armed with these results we analyze the microscopic aspects of HQVs in $UPt_3$ and $Sr_2RuO_4$. We compute the quasiparticle density of states and the local magnetic field around HQVs, which should be accessible to scanning tunneling microscopy (STM), micromagnetometry and neutron scattering below 300 mK.