Two-parameter scaling function for a two-dimensional system

We construct a two-parameter scaling function due to power-law localisation in two dimensions. The scaling function is in good agreement with the experimental βfunction of Davies, Pepper and Kaveh. It is shown that although a diffusive-hopping transition is expected above the mobility edge, this has little effect on the form of the two-parameter scaling function. We also show that transport mechanisms associated with exponentially localised states lead to a β function which contradicts the data. We conclude that the experimental scaling function of DPK strongly supports the existence of a mobility edge with power-law states above it.