Floquet Topological Semimetal with Nodal Helix

Topological semimetal with nodal line is a novel class of topological matter extending the concept of topological matter beyond topological insulators and Weyl/Dirac semimetals. Here, we show that a Floquet topological semimetal with nodal helix can be generated by irradiating graphene or the surface of a topological insulator with circularly polarized light. Nodal helix is a form of nodal line running across the Brillouin zone with helical winding. Specifically, it is shown that the dynamics of irradiated graphene is described by the time Stark Hamiltonian, which can host a Floquet topological insulator and a weakly driven Floquet topological semimetal with nodal helix in the high and low frequency limits, respectively. One of the most striking features of the Floquet topological semimetal at low frequency is that the Berry phase accumulated along the time direction, also known as the Zak phase, has a topological discontinuity of π across the projected nodal helix. It is predicted that such a topological discontinuity of the Berry phase manifests itself as the topological discontinuity of the Floquet states. At intermediate frequency, this topological discontinuity can create an interesting change of patterns in the quasienergy dispersion of the Floquet states.