Fermi Level Fluctuations, Reduced Effective Masses and Zeeman Effect during Quantum Oscillations in Nodal Line Semimetals.

We probe quantum oscillations in nodal line semimetals (NLSM) by considering a NLSM continuum model under strong magnetic field and report the characteristics of the Landau level spectra and the fluctuations in the Fermi level as the field in a direction perpendicular to the nodal plane is varied through. Based on the results on parallel magnetization, we demonstrate the growth of quantum oscillation with field strength as well as its constancy in period when plotted against 1/B. We find that the density of states which show series of peaks in succession, witness bifurcation of those peaks due to Zeeman effect. For field normal to nodal plane, such bifurcations are discernible only if the electron effective mass is considerably smaller than its free value, which usually happens in these systems. Though a reduced effective mass $m^*$ causes the Zeeman splitting to become small compared to Landau level spacing, experimental results indicate a manyfold increase in the Lande $g$ factor which again amplifies the Zeeman contribution. We also consider magnetic field in the nodal plane for which the density of state peaks do not repeat periodically with energy anymore. The spectra become more spread out and the Zeeman splittings become less prominent. We find the low energy topological regime, that appears with such in-plane field set up, to shrink further with reduced $m^*$ values. However, such topological regime can be stretched out in case there are smaller Fermi velocities for electrons in the direction normal to the nodal plane.