Second-harmonic generation in fluctuating Ising superconductors

In a two-dimensional noncentrosymmetric transition metal dichalcogenide Ising superconductor in the fluctuating regime under the action of a uniform external electromagnetic field, a second-harmonic generation effect takes place.
There emerge two contributions to this effect, one conventional, which is due to the electron gas in its normal state, and the other one is of the Aslamazov-Larkin nature. 
Namely, it originates from the presence of fluctuating Cooper pairs in the system when the temperature approaches the temperature of the superconducting transition in the sample from above. 
Employing a usual approach to Ising superconductors, we lift the valley degeneracy by application of a weak out-of-plane external magnetic field, which produces a Zeeman effect. 
In calculations, we use the Boltzmann equations approach for the electron gas in the normal state and the time-dependent Ginzburg-Landau equations for the fluctuating Cooper pairs and show the emergence of second harmonic generation current characterized by temperature-dependent broadening and redshift.