Theoretical Analysis of Kagome Lattices: Optical Conductivity and Heat Capacity

We carry out a theoretical study of the optical and thermal properties of kagome-derived lattices. Using effective low-energy Hamiltonians, we first develop 2×2 matrix models near Dirac and van Hove points to capture symmetry-protected interband transitions, then extend to a full 3×3 matrix tight-binding description to incorporate flat-band effects and their associated anomalies in the optical response. Optical conductivity is computed via the Kubo formalism, emphasizing spectral-weight redistribution and signatures linked to flat bands and topology. Thermal properties are analyzed through the grand thermodynamic potential of a noninteracting Fermi gas using a low-temperature Sommerfeld expansion, revealing heat-capacity trends under gap-opening scenarios and anisotropic behavior. This framework identifies experimentally relevant features-such as THz/IR absorption signatures and flat-band-driven anomalies, providing benchmarks for future measurements and band-engineering strategies using light or strain.