Mirror-protected Majorana zero modes in $f$-wave multilayer graphene superconductors

Abstract: Inspired by recent experimental discoveries of superconductivity in chirally-stacked and twisted multilayer graphene, we study models of $f$-wave superconductivity on the honeycomb lattice with arbitrary numbers of layers. These models respect a mirror symmetry that allows classification of the bands by a mirror-projected winding number $\nu_\pm$. For odd numbers of layers, the systems are topologically nontrivial with $\nu_\pm = \pm 1$. Along each mirror-preserving edge in armchair nanoribbons, there are two protected Majorana zero modes. These modes are present even if the sample is finite in both directions, such as in rectangular and hexagonal flakes. Crucially, zero modes can also be confined to vortex cores, which can be created by a magnetic field or localized magnetic impurities and accessed by local scanning probes. Finally, we apply these models to twisted bilayer and trilayer systems, which also feature boundary-projected and vortex-confined zero modes. Since vortices are experimentally accessible, our study suggests that superconducting multilayer graphene systems are promising platforms to create and manipulate Majorana zero modes.