  Interference between different quantum paths can generate Fano resonance. One
of the examples is transport through a quasibound state driven by
time-dependent scattering potential. Previously it is found that Fano resonance
occurs as a result of energy matching in one-dimensional systems. In this work,
we demonstrate that when transverse motion is present, Fano resonance occurs
precisely at the wavevector matching situation. Using the Floquet scattering
theory, we considered the transport properties of a nonadiabatic time-dependent
well both in the 2DEG and monolayer graphene structure. Dispersion of the
quasibound state of a static quantum well is obtained with transverse motion
present. We found that Fano resonance occurs when the wavevector in the
transport direction of one of the Floquet sidebands is exactly identical to
that of the quasibound state in the well at equilibrium and follows the
dispersion pattern of the latter. To observe the Fano resonance phenomenon in
the transmission spectrum, we also considered the pumped shot noise properties
when time and spatial symmetry secures vanishing current in the considered
configuration. Prominent Fano resonance is found in the differential pumped
shot noise to the reservoir Fermi energy.
