Circulating persistent current and induced magnetic field in a fractal network

TL;DR

This paper investigates the conductance, circulating currents, and magnetic fields in a fractal Sierpinski gasket structure, revealing regularities across generations and effects of anisotropy on transport properties.

Contribution

It provides a detailed analysis of current and magnetic field patterns in a fractal network, highlighting the impact of structural self-similarity and anisotropy on electronic transport.

Findings

Circulating currents and magnetic fields exhibit regular patterns across fractal generations.

Anisotropy in hopping increases the overall transport current.

Physical quantities show self-similar behavior in the fractal structure.

Abstract

We present the overall conductance as well as the circulating currents in individual loops of a Sierpinski gasket (SPG) as we apply bias voltage via the side attached electrodes. SPG being a self-similar structure, its manifestation on loop currents and magnetic fields are examined in various generations of this fractal and it has been observed that for a given configuration of the electrodes, the physical quantities exhibit certain regularity as we go from one generation to another. Also a notable feature is the introduction of anisotropy in hopping causes an increase in magnitude of overall transport current. These features are a subject of interest in this article.