A fractal geometry immersed in a hierarchical magnetic flux distribution

TL;DR

This paper introduces a theoretical model of a Sierpinski gasket fractal with hierarchical magnetic flux, demonstrating how tuning flux parameters can control quantum states and persistent currents, with potential applications in nanoelectronics.

Contribution

It presents a novel model of a fractal with hierarchical magnetic flux, showing how to engineer quantum states and currents by tuning flux parameters.

Findings

Quantum states can be systematically engineered by tuning the hierarchy parameter.

Persistent current in the fractal can be regulated through magnetic flux control.

The model applies across various electronic filling factors.

Abstract

Fractal geometry presents us with a self-similarity in their pattern at various length scales that is prevalent in our natural world. We present theoretical model of a Sierpinski gasket (SPG) fractal geometry with a deterministic perturbation in the form of a hierarchical distribution of magnetic flux. Such flux configuration induces a deterministic disorder in the Aharonov-Bohm (AB) phases picked up by the electron wavefunction. Using the tight-binding formalism, we show that by tunning the strength of the hierarchy parameter of those AB phases, one can systematically engineer quantum states in a SPG fractal lattice. In addition to this, we have also observed that by controlling the strength of this hierarchy parameter in the magnetic flux, one can effectively regulate the persistent current in the SPG fractal structure. This characteristic is found to be true for various filling factors. Our results could be useful for designing nanoelectronic devices using molecular fractal structures fabricated by chemical synthesis technique.