Fragile topology in nodal-line semimetal superconductors

We study the band topology of superconducting nodal-line semimetal (SC-NLSM) protected by inversion symmetry with and without spin-orbital coupling. Without coupling, both $s$-wave SC-NLSM chiral $p$-wave are topologically nontrivial can be described nonzero winding number. Based on Wilson loop method, we verify that they fragile topological superconductors, namely, their topologies moved off coupling to additional trivial bands. The phase persists in spinful system time-reversal when a term is added. For system, second-order superconductors. propose depends strongly degeneracy Majorana zero modes parity gap function. Interestingly, presence vortex line, hosts two pairs stable core.