Physicists build fractal shape out of electrons

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https://phys.org/news/2018-11-physicists-fractal-electrons.html

Physicists build fractal shape out of electrons

November 12, 2018 by Utrecht University, Utrecht University Faculty of Science

 

Electrons in bonding (left) and non-bonding (right) Sierpiński triangles; scale bar 2nm. Credit: Kempkes et al., Nature Physics, 2018

In physics, it is well-known that electrons behave very differently in three dimensions, two dimensions or one dimension. These behaviours give rise to different possibilities for technological applications and electronic systems. But what happens if electrons live in 1.58 dimensions – and what does it actually mean? Theoretical and experimental physicists at Utrecht University investigated these questions in a new study that will be published in Nature Physics on 12 November.

Read more at: https://phys.org/news/2018-11-physicists-fractal-electrons.html#jCp

the paper:

https://www.nature.com/articles/s41567-018-0328-0

Design and characterization of electrons in a fractal geometry:

Abstract:

The dimensionality of an electronic quantum system is decisive for its properties. In one dimension, electrons form a Luttinger liquid, and in two dimensions, they exhibit the quantum Hall effect. However, very little is known about the behaviour of electrons in non-integer, or fractional dimensions1. Here, we show how arrays of artificial atoms can be defined by controlled positioning of CO molecules on a Cu (111) surface2,3,4, and how these sites couple to form electronic Sierpiński fractals. We characterize the electron wavefunctions at different energies with scanning tunnelling microscopy and spectroscopy, and show that they inherit the fractional dimension. Wavefunctions delocalized over the Sierpiński structure decompose into self-similar parts at higher energy, and this scale invariance can also be retrieved in reciprocal space. Our results show that electronic quantum fractals can be artificially created by atomic manipulation in a scanning tunnelling microscope. The same methodology will allow future studies to address fundamental questions about the effects of spin–orbit interactions and magnetic fields on electrons in non-integer dimensions. Moreover, the rational concept of artificial atoms can readily be transferred to planar semiconductor electronics, allowing for the exploration of electrons in a well-defined fractal geometry, including interactions and external fields.