# Confinement of wave-function in Fractal geometry, a detection using DFT

## TL;DR

This paper explores the confinement of electronic wavefunctions in fractal geometries using first-principles methods, demonstrating the design and characterization of fractal lattices like molecular graphene and Lieb lattices.

## Contribution

It introduces a novel application of first-principles methods to study and design electrons in fractal geometries such as Hausdorff dimension lattices.

## Key findings

- Successful modeling of electrons in fractal lattices
- Construction of hexaflake and Vicsek fractals on surfaces
- Potential for high-throughput screening of fractal materials

## Abstract

Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties. The recent work on confinement of the electronic wavefunction in fractal dimensions by creating artificial lattice has given rise to new possibilities of designing artificial lattice. In this study, we demonstrate that the first principle methods can be effectively employed to investigate, design and characterize electrons in Hausdorff dimension. We apply the method to study the molecular graphene and Lieb lattices which lead to fractal lattices based on these fractals. We construct the hexaflake and Vicsek fractals by adsorption of CO molecules on Cu(111) surface. This opens up the possibility of using high throughput techniques for screening and discovering such lattices from currently known crystals or developing them altogether.