Electronic properties and quantum transport in functionalized graphene Sierpinski-carpet fractals

Recent progress in the controllable functionalization of graphene surfaces enables experimental realization complex functionalized nanostructures, such as Sierpinski carpet (SC) fractals. Herein, we model SC fractals formed by hydrogen and fluorine patterns on surfaces, namely, H-SC F-SC, respectively. We then reveal their electronic properties quantum transport features. From calculated results total local densities state, find that states F-SC have two characteristics: (i) low-energy inside about $|E/t|\ensuremath{\le}1$ (with $t$ nearest-neighbor hopping) are localized free regions due to insulating (ii) high-energy special energy ranges including $\ensuremath{-}2.3<E/t<\ensuremath{-}1.9$ with holes only areas $3<E/t<3.7$ electrons fluorinated areas. The characteristics further verified real-space distributions normalized probability density. analyze fractal dimension conductance spectra fluctuations these structures follow Hausdorff dimension. calculate optical conductivity several additional peaks appear adsorbed H or F atoms.