Giant nonlinear response due to unconventional oscillation in Nodal-line semimetals

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.