The Sierpinski triangle (ST) is a fractal mathematical structure that has been used to explore the emergence of flat bands in lattices of different geometries and dimensions in condensed matter. Here we look into fractal features in the electronic properties of ST flakes and molecular chains simulating experimental synthesized fractal nanostructures. We use a single-orbital tight binding model to study the fractal properties of the electronic states and the Landauer formalism to explore transport responses of the quasi 1D molecular chains. The self-similarity of the energy states is found comparing different ST orders and also amplifying the energy ranges investigated, for both flakes and quasi-1D systems. In particular, the results for the local density of states of the theoretical molecular chains proposed here exhibit quite similar spatial charge distribution of experimental STM reports. The analysis of the transport response of such all-carbon fractal molecular chains can be used as a guide to propose a variety of architectures in the synthesis of real new molecular chains.
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