We theoretically investigate the electronic and transport properties of a semi-Dirac material under the influence of an external time-dependent periodic driving field (irradiation) by means of Floquet theory. We explore the inelastic scattering mechanism between different sidebands, induced by irradiation, by using the Floquet scattering matrix approach. The scattering probabilities between the two nearest sidebands depend monotonically on the strength of the amplitude of the irradiation. The external irradiation induces a gap in the band dispersion which is strongly dependent on the angular orientation of momentum. Although the high-frequency limit indicates that the gap opening does not occur in an irradiated semi-Dirac material, a careful analysis of the full band structure beyond this limit reveals that a gap opening indeed appears for higher values of momentum (away from the Dirac point). Furthermore, the angular-dependent dynamical gap is also present and cannot be captured within the high-frequency approximation. The contrasting features of an irradiated semi-Dirac material, in comparison with irradiated graphene, can be probed via the behavior of conductance. The latter exhibits the appearance of nonzero conductance dips due to the gap opening in the Floquet band spectrum. Moreover, by considering a nanoribbon geometry of such a material, we also show that it can host a pair of edge modes which are fully decoupled from the bulk, which is in contrast to the case of a graphene nanoribbon where the edge modes are coupled to the bulk. We also investigate whether, if the nanoribbon of this material is exposed to the external irradiation, decoupled edge modes penetrate into the bulk.

• Received 6 September 2018
• Revised 5 December 2018

DOI:https://doi.org/10.1103/PhysRevB.98.235424