Spin–orbit modulated optical properties in Lieb-to-kagome lattices

We investigate the optical conductivity of two-dimensional flat-band systems undergoing a transition from Lieb to kagome lattice geometries. Using a generalized tight-binding Hamiltonian with intrinsic spin–orbit coupling (ISOC), we compute both the real and imaginary parts of the longitudinal optical conductivity via the Kubo formula. At 1 / 3 and 2 / 3 fillings, we identify key differences in interband transitions between Dirac and flat bands across lattice geometries. In the Lieb lattice, Dirac-to-Dirac transitions are symmetry-forbidden, while Dirac-to-flat band transitions dominate. In contrast, the kagome lattice supports both Dirac-to-Dirac and Dirac-to-flat transitions, resulting in a broadened optical response that extends into the ultraviolet regime. ISOC opens non-trivial gaps at Dirac and Γ points, enabling direct optical estimation of the ISOC-induced gap and enhancing transition strengths by factors up to two. Our results demonstrate how lattice geometry and ISOC jointly govern flat-band optical responses, with implications for tunable optoelectronic and plasmonic applications in two-dimensional kagome-based materials. • Lieb–Kagome Framework: Unified tight-binding model compares flat-band. • Spin–Orbit Effects: Intrinsic SOC opens gaps at Dirac and Γ points. • Optical Conductivity: Longitudinal real and imaginary parts computed via Kubo. • Transition Pathways: Lieb allows Dirac–flat; kagome allows Dirac–Dirac too. • Geometry Control: Lattice geometry and SOC tune spectra for light–matter control.