  Considering models with tilted linear and quadratic band touching
dispersions, we analyze the effect of the transverse linear tilt on the
transmission spectra through a harmonically driven potential well oriented
longitudinally. Employing the Floquet scattering matrix formalism, we find Fano
resonances as an outcome of matching between the Floquet sidebands and
quasi-bound states, where the tilt renormalizes their energies and wave
vectors. We find that the Fano resonance energy decreases (increases) for
linear (quadratic) band touchings as the magnitude of the transverse momentum
increases, indicating a distinct signature of the underlying band dispersion in
the transmission profile. The sign of the product of the transverse momentum
and the tilt also determines the relative shift in the Fano resonance energy
with respect to the untilted case for both band dispersions, suggesting a
possible tunability of the Fano resonance for tilted systems. Importantly, the
tilt strength can also be directly determined by measuring the Fano resonance
energy as function of the transverse momenta direction. We furthermore study
the shot noise spectra and their differential property where we find an
inflection region and undulation, respectively, around the Fano resonance
energy. Interestingly, differential shot noise and transmission spectra both
qualitatively behave in a similar fashion and might thus serve as important
observables for future experiments on driven solid-state systems.
