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NANOSCIENCE

Quantum fractals

Nature Physics volume 15, pages 111–112 (2019)Cite this article

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Electrons with fractional dimension have been observed in an artificial Sierpiński triangle, demonstrating their quantum fractal nature.

Fractals, first named by mathematician Benoit Mandelbrot1 in 1975, are never-ending complex patterns that look the same whether seen from near or far. These irregular shapes show the same degree of non-regularity on all scales. The Romanesco broccoli, the nautilus shell and the network of veins in the human body are natural examples that show the self-repeating characteristics of fractals. Now, reporting in Nature Physics, Sander Kempkes and collaborators2 present a spectroscopic characterization of the electronic wavefunction inside a confined structure with fractal geometry, and demonstrate that the electrons inside it live in a space with fractional dimension.

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Fig. 1: Sketch of the first three generations of the Sierpiński triangle.

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Authors and Affiliations

  1. Donostia International Physics Center, Donostia–San Sebastian, Spain

    Dario Bercioux

  2. University of the Basque Country, UPV/EHU, Bilbao, Spain

    Ainhoa Iñiguez

Authors
  1. Dario Bercioux
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  2. Ainhoa Iñiguez
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Correspondence to Dario Bercioux or Ainhoa Iñiguez.

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Bercioux, D., Iñiguez, A. Quantum fractals. Nature Phys 15, 111–112 (2019). https://doi.org/10.1038/s41567-018-0327-1

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