Andrea Tomadin — NEST-CNR & SNS Pisa #
Transport and optical properties of an electron gas in a Sierpinski carpet #
Recent progress in the design and fabrication of artificial two-dimensional (2D) materials paves the way for the 
experimental realization of electron systems moving on plane fractals. In this work, we present the results of 
computer simulations for the conductance and optical absorption spectrum of a 2D electron gas roaming on a 
Sierpinski carpet, i.e. a plane fractal with Hausdorff dimension intermediate between one and two. We find that the 
conductance is sensitive to the spatial location of the leads and that it displays fractal fluctuations whose 
dimension is compatible with the Hausdorff dimension of the sample. Very interestingly, electrons in this fractal 
display a broadband optical absorption spectrum, which possesses sharp "molecular" peaks at low photon energies.