Electronic fractal patterns in building Sierpinski-triangles molecular systems

TL;DR

This paper investigates the electronic properties of Sierpinski Triangle fractal structures in molecular systems, revealing self-similar energy states and transport behaviors that align with experimental observations, guiding future molecular nanostructure synthesis.

Contribution

It introduces a theoretical study of electronic and transport properties in fractal Sierpinski Triangle molecular systems, connecting fractal geometry with electronic behavior and experimental STM data.

Findings

Self-similar energy states across different fractal orders

Local density of states matches experimental STM charge distributions

Transport responses suggest new molecular chain architectures

Abstract

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 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 are 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 transport response of such all-carbon fractal molecular chains can be used as a guide to propose a variety of architecture in the synthesis of real new molecular chains.