Half quantum vortices and Majorana fermions in triplet superconductors

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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 UPt₃, Sr₂RuO₄ and U₁₋ₓThₓBe₁₃ 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 UPt₃, Sr₂RuO₄ and CePt₃Sn. Armed with these results we analyze the microscopic aspects of HQVs in UPt₃ and Sr₂RuO₄. 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.