  Quantum oscillations in magnetoconductance of a material at low temperatures
and in presence of an intense magnetic field are described by the Shubnikov de
Haas (SdH) effect. It is widely assumed to be the hallmark of the Fermi surface
of a given metal. In contrast to the canonical situation, we identify an exotic
oscillation in nonlinear responses of three-dimensional nodal line semimetals
(NLSMs) which persist even at temperatures where the typical SdH-like
oscillations vanish. This oscillation occurs due to the periodic gap-closing of
a pair of Landau levels at zero Fermi energy with the variation of the magnetic
field. The emergence of the oscillation is a remarkable fingerprint of ring
dispersion and the corresponding frequency can be used to determine the radius
of the ring. Using the Boltzmann equation, we calculate the second harmonic
generation of nodal line semimetals under parallel DC electric and strong
magnetic fields. The second harmonic conductivity diverges at the gap closing
condition leading to the giant nonlinear response in NLSMs.
