Floquet engineering of gapped Dirac and triplet band structure with topological insulating phase induced by light irradiation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>β</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:

We theoretically investigated the effects of high-frequency circularly polarized light (CPL) on the electronic properties of ${\ensuremath{\beta}}_{12}$ borophene system via Floquet engineering. The Floquet indirect electron hoppings enable the phase of the Dirac and triplet fermions in borophene modulated by light irradiation. First, we built the low-energy effective two-band model and three-band model to describe the photon-assisted electron behaviors analytically. We found that the gapped Dirac fermions harbor valley-dependent feature as well as the topological insulating phase transition between quantum anomalous Hall (QAH) and quantum valley Hall. Then we employ strong CPL to eliminate the inherent metallic phase in bulk of ${\ensuremath{\beta}}_{12}$ borophene nanoribbon, which becomes topological QAH insulator. Furthermore, the corresponding local current distributions are plotted in real space with the chiral edge state indicating QAH phase. The results show that the CPL-induced chiral edge states are topologically protected and robust in spite of the choice of parameter models and different edge configurations of the nanoribbons. Apart from developing the analysis of gapped Dirac and triplet fermions in borophene, our results with the semiconducting band and topological insulating phase induced by CPL may pave the way for the realization of ${\ensuremath{\beta}}_{12}$-borophene-based valleytronic and optoelectronic devices.