Quasi-one-dimensional carbon-based fractal lattices

Abstract

Fractal systems are now considered alternative routes for engineering physical properties on the nanoscale. In particular, stable annular quantum corrals have been demonstrated in distinct synthesis procedures and can provide interesting localized and resonant states. We here present a theoretical description of effective fractal lattices, mainly composed of annular Koch geometries based on carbon atoms, and of more complex organic molecules described by triangular Sierpinski geometries. A single band tight-binding approach is considered to derive electronic and transport properties. Fractal molecular linear chains composed of fractal Koch quantum corrals are proposed, and their electronic transport is discussed based on the complexity of the neighboring hopping. The spatial charge distributions at different energies highlight the contribution of the composing metallic and carbons atoms in the quantum corral features, serving as a guide to new functionalization applications based on the symmetry and fractal peculiarities of the proposed nanostructured lattices.