Electrical resistance of complex two-dimensional structures of loops

This work presents a study of the dc electrical resistance of a recently discovered hierarchical two-dimensional system which has a complex topology consisting of a distribution of disordered macroscopic loops with no characteristic size and a distribution of several types of contacts between loops. In addition to its intrinsic interest in the important context of low-dimensional systems and crumpled systems, the structures under study are of relevance in a number of areas including soft condensed matter and packing of DNA in viral capsids. In the particular case discussed here, the loops are made of layers of graphite with a height of tens of nanometers deposited on a substrate of cellulose. Experiments with these systems indicate an anomalous electrical resistance of sub-diffusive type. The results reported here are explained with scaling arguments and computer simulation. A comparison with the dc electrical properties of percolation clusters is made, and some other experimental issues as future prospects are commented.