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

TL;DR

This paper explores $f$-wave superconductivity in multilayer graphene, revealing mirror symmetry-protected Majorana zero modes at edges and vortex cores, with implications for quantum computing applications.

Contribution

It introduces a topological classification of $f$-wave superconducting multilayer graphene respecting mirror symmetry, identifying conditions for Majorana zero modes at edges and vortices.

Findings

Odd-layer systems are topologically nontrivial with protected zero modes.

Majorana zero modes are present at edges and vortex cores.

Vortices can be created and manipulated via magnetic fields or impurities.

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.