Transport properties of a topological system in non-integer dimensions

In recent years, the subject of topological materials has inspired a very active field of research. A considerable amount of effort was put into investigating the stability of topological edge modes under various kinds of disturbances, such as disorder.
Another less explored avenue is the stability of edge modes under variation of the dimensionality. By putting a topological system on a lattice with fractal geometry and considering and investigating the transport properties we are able to detect the influence of non-integer dimensionality on the topological properites and stability of the system.