Mysteries of the quantum Hall staircase
Quantum Hall effects are a very rich subject in condensed matter physics with many connections to other areas, intrinsic intellectual beauty, and numerous applications. After more than 35 years after the initial discovery, there are new surprising and unexpected phenomena being discovered in this area, both in experiments and in theory. A visual manifestation of the effects is the plot of the Hall resistance as a function of magnetic field, featuring prominent, precisely quantized steps, also called plateaux, and thereby resembling a staircase. The walk up this staircase is a journey in time, where every step needs new ideas and concepts, leading up to cutting edge research in topological phases of matter and quantum information processing, but also to the soon-to-be-implemented new standard of mass. Staring with the original discovery by Edwin Hall in 1879, I will try to explain the basic features of the quantum Hall staircase. I will then focus on one of the unsolved mysteries: the problem of the transitions between plateaux with different values of the Hall conductivity, and the associated critical behavior.