Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet–Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

Ultrafast materials science promises optical control of physical properties of solids. Continuous-wave circularly polarized laser driving was predicted to induce a light-matter coupled state with an energy gap and a quantum Hall effect, coined Floquet topological insulator. Whereas the envisioned Floquet topological insulator requires high-frequency pumping to obtain well-separated Floquet bands, a follow-up question regards the creation of Floquet-like states in graphene with realistic low-frequency laser pulses. Here we predict that short optical pulses attainable in experiments can lead to local spectral gaps and novel pseudospin textures in graphene. Pump-probe photoemission spectroscopy can track these states by measuring sizeable energy gaps and Floquet band formation on femtosecond time scales. Analysing band crossings and pseudospin textures near the Dirac points, we identify new states with optically induced nontrivial changes of sublattice mixing that leads to Berry curvature corrections of electrical transport and magnetization.