Anomalous Goos-Hänchen shift in the Floquet scattering of Dirac fermions

We study the inelastic scattering of two-dimensional massless Dirac fermions by an inhomogeneous time-dependent driving field. As a physical realization, we consider a monolayer graphene normally illuminated with a circularly polarized laser of frequency Ω in a given region. The interaction Hamiltonian introduced by the laser, being periodic in time, can be treated with the Floquet method, which naturally leads to a multichannel scattering problem. We analyze planar and circular geometries of the interface separating the irradiated and nonirradiated regions and find that there is an anomalous Goos-H\"anchen shift in the inelastic channel. The latter is weakly dependent on the amplitude of the driving (for small amplitudes) while its sign is determined by the polarization of the laser field. We related this shift with the appearance of topological edge states between two illuminated regions of opposite chiralities.