This study investigates the square-octagon lattice electronic properties and quantum capacitance under various external parameters, including hopping amplitudes, magnetic flux, and on-site Coulomb repulsion (OSCRI) by using the Hubbard model (HM) and Green function. The analysis reveals that the lattice can exhibit tunable electronic behaviors, transitioning between semiconducting, metallic and insulating states by adjusting the hopping parameter ratio t2/t1. Specifically, for t2 = t1 and t2 = 3t1, the material remains semiconducting, while for t2 = 2t1, it behaves as a metal. The application of magnetic flux reduces the band gap for t2 = t1 and t2 = 3t1 while increasing it for t2 = 2t1. Magnetic flux also shifts the flat band's position in all cases. Additionally, increasing the OSCRI (from 0.5 eV to 1.5 eV) leads to energy level splitting, breaking the symmetry of degenerate states, and widening the band gap. The quantum capacitance is strongly influenced by these parameters, with the peak intensity decreasing with increasing magnetic flux and shifting toward negative gate potentials. The results highlight the square-octagon lattice tunability in both electronic states and charge storage capabilities, making it a promising candidate for applications in nanoelectronics and energy storage devices where precise control over electronic properties is essential.
