Transport and optical properties of an electron gas in a Sierpinski carpet

TL;DR

This study uses computer simulations to explore how electrons behave in a 2D fractal structure called a Sierpinski carpet, revealing unique conductance and optical properties linked to the fractal geometry.

Contribution

It provides the first detailed simulation analysis of electron transport and optical absorption in a Sierpinski carpet, highlighting fractal-dependent conductance fluctuations and broadband absorption features.

Findings

Conductance is sensitive to lead placement and shows fractal fluctuations.

Optical absorption spectrum has sharp peaks at low photon energies.

Electron behavior reflects the fractal geometry of the Sierpinski carpet.

Abstract

Recent progress in the design and fabrication of artificial two-dimensional (2D) materials paves the way for the experimental realization of electron systems moving on plane fractals. In this work, we present the results of computer simulations for the conductance and optical absorption spectrum of a 2D electron gas roaming on a Sierpinski carpet, i.e. a plane fractal with Hausdorff dimension intermediate between one and two. We find that the conductance is sensitive to the spatial location of the leads and that it displays fractal fluctuations whose dimension is compatible with the Hausdorff dimension of the sample. Very interestingly, electrons in this fractal display a broadband optical absorption spectrum, which possesses sharp "molecular" peaks at low photon energies.