Fragile topology in nodal-line semimetal superconductors

TL;DR

This paper investigates the fragile topological properties of superconducting nodal-line semimetals, revealing their dependence on symmetry, spin-orbit coupling, and vortex states, and identifying their potential for hosting Majorana zero modes.

Contribution

It demonstrates that SC-NLSMs exhibit fragile topological phases that are sensitive to additional trivial bands and explores their behavior with spin-orbit coupling and vortex states.

Findings

Both s-wave and p-wave SC-NLSMs are topologically nontrivial without spin-orbit coupling.

Fragile topology persists in spinful systems with time-reversal symmetry and spin-orbit coupling.

Spinful s-wave SC-NLSM hosts two pairs of Majorana zero modes in vortex cores.

Abstract

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