##### Atom-by-atom engineering of novel states of matter

Cristiane Morais Smith

Feynman’s original idea of using one quantum system that can be manipulated at will to simulate the behavior 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 nanophotonics and in condensed matter. In this talk, I will discuss a few recent experiments, in which 2D electron lattices were engineered on the nanoscale using STM manipulation of adatoms on the surface of copper. First, I will show that it is possible to control the geometry of the lattice [1] and the orbital degrees of freedom [2] by building different Lieb lattices [1,2]. Then, I will show how to realize topological states of matter using the same procedure. We investigate the robustness of the zero modes in a breathing Kagome lattice, which is the first experimental realization of a designed electronic higher-order topological insulator [3], and the fate of the edge modes in a Kekule structure, upon varying the type of boundary of the sample [4]. Finally, we will control the effective dimension of the electronic structure by creating a Sierpinski gasket [5-7], which has dimension D = 1.58. The realization of this first quantum fractal opens the path to electronics in fractional dimensions. In addition, our recent investigation of quantum transport in fractals by using photonic quantum simulators might shed some light on the issue of consciousness