Floquet scattering of quadratic band-touching semimetals through a time-periodic potential well.

We consider tunneling of quasiparticles through a rectangular quantum well, subject to periodic driving. The quasiparticles are the itinerant charges in two-dimensional and three-dimensional semimetals having a quadratic band touching (QBT) point in the Brillouin zone. We assume a non-adiabatic limit where the Floquet theorem is applicable to analyze the time-periodic Hamiltonian. By deriving the Floquet scattering matrices, we chalk out the transmission and shot noise spectra of the QBT semimetals. The spectra show Fano resonances, which we identify with the (quasi)bound states of the systems.