Design and Characterization of Electronic Fractals

The dimensionality and geometry of a quantum system are decisive factors for its electronic properties. So far, research has focused on systems with integer dimensions ranging from 0D to 3D. However, very little is known about the properties of electrons in fractional dimensions. This is because geometrical fractals, although pervasive in our everyday life, remain elusive in the quantum world. One possible route to create electronic quantum fractals is by confining the surface state electrons of Cu(111) by accurate positioning of adsorbed CO molecules [1,2]. Here, we realize and characterize an electronic Sierpiński triangle fractal with dimension 1.58. Using scanning tunneling spectroscopy and wave-function mapping, we observe single-electron wave functions with a fractal dimension derived from the Sierpiński geometry. These results bear importance for the understanding of the transport properties of and charge storage in fractal-like structures, opening the path to fractal-dimension electronics in a systematic and controlled manner.

1. K.K. Gomes et al., Nature 483, 306–310 (2012)
2. M.R. Slot et al., Nature Physics 13, 672-676 (2017)