Floquet engineering of titled and gapped Dirac materials

We have established a rigorous theoretical formalism for Floquet engineering, or investigating and eventually tailoring most crucial electronic properties of tetragonal molybdenum disulfide (1T$^\prime$-MoS$_2$), by applying an external high-frequency dressing field in the off-resonant regime. It was recently demonstrated that monolayer semiconducting1T$^\prime$-MoS$_2$ may assume a distorted tetragonal structure which exhibits tunable and gapped spin- and valley-polarized tilted Dirac bandstructure. From the viewpoint of electronics, 1T$^\prime$-MoS$_2$ is one of the most technologically promising nanomaterials and a novel representative of an already famous family of transition metal dichalcogenides. The obtained dressed states strongly depend on the polarization of the applied irradiation and reflect the full complexity of the initial low-energy Hamiltonian of non-irradiated material. We have calculated and analyzed the obtained electron dressed states for linear and circular types of the polarization of the applied field focusing on their symmetrical properties, anisotropy, tilting and bandgaps, as well as topological signatures. Since a circularly polarized dressing field is also known to induce a transition into a new state with broken time-reversal symmetry and a non-zero Chern number, the combination of these topologically non-trivial phases and transitions between them could reveal some truly unique and earlier unknown phenomena.