Majorana-Weyl cones in ferroelectric superconductors

It has been theoretically shown that non-trivial topological superconductivity can be realized based on s-wave superconductivity, Rashba spin-orbit coupling, and a sufficiently strong magnetic field. We revisit this scenario in the context of 3D ferroelectric superconductors, e.g., SrTiO₃. First, we show that for a uniform Zeeman field, two or four Majorana-Weyl cones emerge when the field exceeds a critical value. We further show the Weyl cones can be tilted by tuning the angle between the ferroelectric polarization and the Zeeman field and may even "over-tilt" and become type-II Weyl points with Bogoliubov Fermi surfaces. We also show that tetragonal domain walls can, in some cases, become interfaces between domains characterized by opposite Majorana-Weyl cones' chiralities. Such domain walls will then host Majorana zero modes inside the specimen. To account for the realistic scenario, we then consider the orbital effect of the magnetic field. We show that single superconducting vortices are surrounded by topological "halos" hosting Majorana arc states on their outer boundaries and in their centers. As the value of the magnetic field increases, the density of the vortices grows, which leads to the overlapping of the topological "halos" and, eventually, to the percolation of the topological phase throughout the system. In the end, we discuss some experimental probes to test our predictions.