Giant nonlinear response due to unconventional magneto-oscillations in nodal-line semimetals

Nodal-line semimetals (NLSMs) support many exotic phenomena due to the unique torus-shaped Fermi surfaces in their band structure. We study the nonlinear responses of three-dimensional NLSMs in the presence of parallel dc electric and strong magnetic fields using the Boltzmann equation. At zero temperature, the second harmonic conductivity is found to exhibit $1/B$-periodic quantum oscillations which are akin to the Shubnikov--de Haas (SdH) oscillations. More interestingly, we uncover an exotic oscillation in nonlinear responses which persists even at temperatures where the typical SdH-like oscillations vanish. This oscillation originates from 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. The second harmonic conductivity diverges at the gap closing points leading to the giant nonlinear response in NLSMs at finite temperature.