Half quantum vortices and Majorana fermions in triplet superconductors

TL;DR

This paper explores the existence and properties of half quantum vortices and Majorana fermions in triplet superconductors, providing theoretical insights and predictions for experimental detection methods.

Contribution

It offers a detailed analysis of HQVs and Majorana fermions in triplet superconductors, including spectral calculations and experimental signatures, advancing understanding of topological excitations in these materials.

Findings

Zero modes of Majorana fermions identified in certain triplet superconductors

Computed quasiparticle density of states around HQVs

Predicted local magnetic field signatures detectable by STM and neutron scattering

Abstract

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.