Temperature dependence of vertical transport in quantum Hall multilayers

We study the temperature dependence of vertical transport in GaAs/Al0.1Ga0.9As multilayers, in the regime of the integer quantum Hall effect. At low temperatures, vertical transport in quantum Hall states occurs on a two-dimensional chiral sheath of edge states near the sidewalls of the sample mesas. At higher temperatures, variable-range hopping through the bulk of the sample dominates. To extend the temperature range of sheath-dominated transport, we increase the device perimeters using fractal-shaped mesas defined by e-beam lithography. We report on the freeze-out of bulk transport and the nearly linear increase of the sheath conductivity with temperature.