  In mesoscopic physics, the application of a time-periodic drive leads to
novel transport behaviour, which is absent in the static regimes. Here we
consider a quantum pumping protocol, such that the quasiparticles of
Weyl/multi-Weyl and nodal-line semimetals are subjected to a time-periodic
rectangular potential well. The presence of an oscillating potential of
frequency $\omega$ creates equispaced Floquet side-bands with spacing $\hbar
\omega$. As a result, a Fano resonance is observed when the difference in the
Fermi energy (i.e., the energy of the incident quasiparticle), and the energy
of one of the (quasi)bound state levels of the well, coincides with the energy
of an integer number of photons (each carrying energy quantum $\hbar \omega$,
equal to the side-band spacing). Using the Floquet theory and the scattering
matrix approach, in the zero-temperature non-adiabatic pumping limit, we find
characteristic Fano resonance patterns in the transmission coefficients, which
depend on the nature of the dispersion. The inflection points in the pumped
shot noise spectra also serve as a proxy for the corresponding Fano resonances.
Therefore, we also numerically evaluate the pumped shot noise. Finally, we
correlate the existence of the Fano resonance points to the (quasi)bound states
of the well, by explicitly calculating the bound states of the static well
(which are a subset of the bound states of the driven system). Since we
consider semimetals with anisotropic dispersions, all the features observed
depend on the orientation of the potential well. We believe that our results
will serve as a guide for future experiments investigating quantum transmission
in nonequilibrium settings.
