Fragile topology in nodal-line semimetal superconductors

Abstract The fragile topological phase is an exotic phase with unstable edge states. Its nontrivial band topology can be removed by coupling to additional topologically trivial bands. Here we reveal that the fragile band topology can be realized in the inversion symmetric odd parity superconducting nodal line semimetal (SC-NLSM) materials with and without the spin orbital coupling. Without the spin orbital coupling, both the s -wave SC-NLSM and the p -wave SC-NLSM host a pair of Majorana zero modes on the system surface. For the spinful case, it has fourfold inverted bands and generates fourfold degenerate Majorana surface/edge states. However, we verify that for all of the systems we considered, they belong to the fragile topological superconducting system based on the Wilson loop method. The vortex bound states are studied numerically and the results depend strongly on the systems.