Floquet engineering of topological semimetals with bicircularly polarized light

Abstract 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, η , in such a way that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>r</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>η</mml:mi> </mml:mrow> </mml:math> , 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 η . Overall, our analytical and numerical results establish BCL as a versatile tool for obtaining tunable topological phases which can be potentially observed in future experiments with BCL.