Band structure evolution from kagome to Lieb under periodic driving field

We theoretically investigate the light-induced transition of the kagome quasienergy spectrum to the Lieb like band structure under periodic driving fields. A generalized framework for the renormalized hopping potential is derived, applicable to any two-dimensional lattice with arbitrary field polarizations. By applying this framework to a kagome lattice driven by linearly polarized light in off-resonant condition, we demonstrate the ability to tune the hopping strength along specific bonds to zero. This tuning induces the merging of Dirac points at high-symmetry points in the Brillouin zone, governed by the field parameters. At specific parameter values, this merging facilitates a transition from the kagome quasienergy spectrum to the Lieb band structure with reduced bandwidth. Our results highlight the critical role of controlled electron hopping in driving this electronic transition, offering valuable insights into the manipulation of electronic properties in periodically driven systems.