Absence of Quantum Oscillations in Nodal Loop Semimetals*

Nodal loop semimetals are three dimensional (semi)metallic systems where the valence and conduction bands closest to the Fermi level cross each other forming a loop in momentum space. In general, any metallic system placed under the effect of a magnetic field display quantum oscillations when electrons move along cyclotron orbits. The scape of Landau levels from the filled Fermi sea (the Lifshitz-Kosevich theory) accounts for these oscillations in several observables, as the Shubnikov de Haas oscillations in the conductivity.
Here we will show how nodal loop semimetals might challenge the LK picture for metals by showing that quantum oscillations are absent at some critical value and orientation of the magnetic field.