# Anomalous Goos-H\"anchen shift in the Floquet scattering of Dirac fermions

## TL;DR

This paper investigates the inelastic scattering of Dirac fermions in graphene under a circularly polarized laser, revealing an anomalous Goos-H"anchen shift linked to topological edge states, independent of laser amplitude.

## Contribution

It introduces a Floquet scattering framework for Dirac fermions in a time-dependent field, uncovering a novel anomalous shift related to topological phenomena.

## Key findings

- Discovered an anomalous Goos-H"anchen shift in inelastic scattering channels.
- The shift's sign depends on laser polarization, not amplitude.
- Linked the shift to the emergence of topological edge states.

## Abstract

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 $\Omega$ 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 multi-channel scattering problem. We analyze planar and circular geometries of the interface separating the irradiated and non-irradiated regions and find that there is an anomalous Goos-H\"anchen shift in the inelastic channel. The latter is independent of the amplitude of the driving 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.