Floquet engineering of topological semimetals with bicircularly polarized light

We study the effect of illumination of bicircularly polarized light (BCL) on topological semimetals, namely multifold fermion and line-node semimetals. We demonstrate, by means of both low-energy and lattice models, that the band-structures of both multifold fermions and line-node semimetal exhibit rich features with BCL illumination. For multifold fermions, we show that if the relative amplitude, $r$, between the two frequency components of the BCL is related to the relative frequency, $\eta$, in such a way that $r^2 = \eta$, then the band touching points remain unchanged without any shift or band gap opening for any choice of the material-dependent parameters. For other choices of the BCL parameters, we find both gapped phases as well as gapless phases with shifted band touching points. Line-node semimetals also exhibit diverse phases, ranging from protected line-nodes under illumination to point nodes, by tuning the BCL parameters $r$ and $\eta$. Overall, our analytical and numerical results establish BCL as a versatile tool for obtaining tunable topological phases.