Feynman’s original idea of using one quantum system that can be controlled and manipulated at will to simulate the behaviour of another more complex one has flourished during the last decades in the field of cold atoms. More recently, this concept started to be developed in nano photonics and in condensed matter. In this talk, I will  discuss a few recent experiments, in which 2D electron lattices were engineered on the nanoscale.  The first is the Lieb lattice [1], and the second is a Sierpinski gasket [2]. The realisation of fractal lattices opens up the path to electronics in fractional dimensions.

At the end, I will discuss some ongoing projects on orbitronics and topological states. 

References

1. [1] M. R. Slot, T. S. Gardenier, P. H. Jacobse, G. C. P. van Miert, S. N. Kempkes, S. J. M. Zevenhuizen, C. Morais Smith, D. Vanmaekelbergh, and I. Swart
   ”Experimental realisation and characterisation of an electronic Lieb lattice”
   Nature Physics 13, 672 (2017) 
2. [2] S. N. Kempkes, M. R. Slot, S. E. Freeney, S. J. M. Zevenhuizen, D. Vanmaekelbergh, I. Swart, and C. Morais Smith, “Design and characterization of electronic fractals, arXiv:1803.04698 (2018), to appear in Nature Physics (2018).