Non-universal edge state physics in the quantum Hall effect

General background -The past decades have seen an almost inexorable move towards universal physics, at the expense of interest in details.The great success of the renormalisation group and the principles of hydrodynamics have underpinned a systematic and powerful understanding of collective phenomena in the limit of long time-and lengthscales.For these insights it is often neither necessary, nor even particularly useful, to dwell too much on what's going on on the lattice scale.This development has been reinforced further by the advent of the notion of topology.Certain phenomena, most prominently Klitzing's quantised Hall conductance e 2 /h, are not only absolutely stable in the sense of being impervious to just about any reasonable local perturbation.Rather, they are so robust that a quantitative calculation on a wrong microscopic model will give a 'correct' result for the topologically protected quantity under consideration.By 'wrong' here I mean studying a model whose microscopic properties are in fact at qualitative variance with what actually happens in experiment.A counterveiling trend to these developments has been set by the availability of increasingly powerful experimental probes, in particular those emanating from nanophysics.Concretely, the availability of micro-SQUIDS or NV-centres on a tip allows the measurement of magnetic fields, and hence the inference of current density distributions, on (even sub)micron lengthscales, while nanopatterning allows for increasing microscopic control on the nanoscale.It is thus natural to ask questions about the physics these probes unveil, much of which takes place away from the universal/topological physics mentioned above, in the sense that it contains genuinely additional information beyond long time and lengthscales.