Crossing points of nodal lines in topological semimetals and the Fermi surface of ZrSiS

We investigate the electron spectra, Fermi surfaces, and their characteristics near crossing points of two band-contact lines in nodal-line semimetals. In particular, the extremal cross-sectional areas and the appropriate cyclotron masses are calculated. We also find the phase of the quantum oscillations associated with the electron orbits near the crossing point. The analysis of all these quantities is carried out both without and with consideration of the spin-orbit interaction. To illustrate the obtained results, we apply them to ZrSiS, in which the crossing of the nodal lines occurs.