Real spin and pseudospin topologies in the noncentrosymmetric topological nodal-line semimetal CaAgAs

We present the topology of spin-split Fermi surface of CaAgAs as determined by de Haas-van Alphen (dHvA) effect measurements combined with ab initio calculations. We have determined the torus-shaped nodal-line Fermi surface from the dHvA oscillations of $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ orbits. The former orbit encircles the nodal line, while the latter does not. Nevertheless, a nontrivial Berry phase is found for both orbits. The nontrivial phase of $\ensuremath{\beta}$ arises from the orbital characters, which can be expressed as a pseudospin rotating around the nodal line. On the other hand, the phase of $\ensuremath{\gamma}$ is attributed to the vortex of real spin texture induced by an antisymmetric spin-orbit interaction. Our result demonstrates that both the real spin and pseudospin textures are indispensable in interpreting the electronic topology in noncentrosymmetric nodal-line semimetals.