Quantum fractals

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

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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


  1. 1.

    Mandelbrot, B. B. The Fractal Geometry of Nature (W. H. Freeman & Co., New York, 1982).

  2. 2.

    Kempkes, S. N. et al. Nat. Phys. (2018).

    ADS  Article  Google Scholar 

  3. 3.

    Crommie, M. F., Lutz, C. P. & Eigler, D. M. Science 262, 218–220 (1993).

    ADS  Article  Google Scholar 

  4. 4.

    Hofstadter, D. R. Phys. Rev. B 14, 2239–2249 (1976).

    ADS  Article  Google Scholar 

  5. 5.

    Dean, C. et al. Nature 497, 598–602 (2013).

    ADS  Article  Google Scholar 

  6. 6.

    Pan, W. et al. Phys. Rev. Lett. 90, 016801 (2003).

    ADS  Article  Google Scholar 

  7. 7.

    Newkome, G. R. et al. Science 312, 1782–1785 (2006).

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    Shang, J. et al. Nat. Chem. 7, 389–393 (2015).

    Article  Google Scholar 

  9. 9.

    Vijay, S., Haah, J. & Fu, L. Phys. Rev. B. 94, 235157 (2016).

    ADS  Article  Google Scholar 

Download references

Author information



Corresponding authors

Correspondence to Dario Bercioux or Ainhoa Iñiguez.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bercioux, D., Iñiguez, A. Quantum fractals. Nature Phys 15, 111–112 (2019).

Download citation

Further reading