Helical Majorana fermions at the interface of Weyl semimetal and d-wave superconductor: Application to Iridates and high-Tc Cuprates

Majorana bound states exist inside a core of half-quantum vortex in spin-triplet superconductors. Despite intense efforts, they have not been discovered in any spin-triplet superconductor candidate materials. After the success of topological insulator, another route to achieve Majorana fermions has been suggested: heterostructures of s-wave superconductors and topological insulator or semimetal with strong spin-orbit coupling provide an effective spinless $p+ip$ pairing which supports Majorana bound states in a single vortex. This theoretical observation has stimulated both experimental and theoretical communities to search for Majorana fermions, and recently a localized Majorana state at the end of one-dimensional wire has been reported. Here we study the two-dimensional interface of Weyl semimetal and d-wave superconductor which promotes a pair of helical Majorana fermions propagating along the edge of the interface. We suggest that Iridium oxide layer IrO$_2$ classified as two-dimensional Weyl semimetal in close proximity to high temperature Cuprates would be a best example to explore these helical Majorana modes.