Design and characterization of electrons in a fractal geometry
Publication date
2018
Authors
Kempkes, S. N.
Slot, Marlou R.
Freeney, Saoirsé E.
Zevenhuizen, S. J. M.
Vanmaekelbergh, D.
Swart, I.
de Morais Smith, C.
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Document Type
Letter
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Abstract
The dimensionality of a quantum system plays a decisive role in its electronic spectral and transport properties. In 3D, electrons behave as a non-interacting Fermi liquid, whereas in 1D interactions are relevant. On the other hand, in 2D exotic phenomena such as charge fractionalization may occur. However, very little is known about electrons in fractional dimensions. Here, we design and characterize an electronic Sierpinski triangle fractal in real and reciprocal space by confining the surface-state electrons of Cu(111) with adsorbed CO molecules. We observe single-electron wave functions in real space with a fractal dimension of 1.58 as well as a subdivision of the wave function in self-similar parts. These results open the path to fractal electronics in a systematic and controlled manner.
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Citation
Kempkes, S N, Slot, M R, Freeney, S E, Zevenhuizen, S J M, Vanmaekelbergh, D, Swart, I & Smith, C M 2018, 'Design and characterization of electrons in a fractal geometry', Nature Physics, vol. 15, no. 2, pp. 127–131. https://doi.org/10.1038/s41567-018-0328-0