Local current distribution and hot spots in the integer quantum Hall regime

In a recent experiment, the local current distribution of a two-dimensional electron gas in the quantum Hall regime was probed by measuring the variation of the conductance due to local gating. The main experimental finding was the existence of "hot spots," i.e., regions with a high degree of sensitivity to local gating, whose density increases as one approaches the quantum Hall transition. However, the direct connection between these hot spots and regions of high current flow is not clear. Here, based on a recent model for the quantum Hall transition consisting of a mixture of perfect and quantum links, the relation between the hot spots and the current distribution in the sample has been investigated. The model reproduces the observed dependence of the number and sizes of hot spots on the filling factor. It is further demonstrated that these hot spots are not located in regions where most of the current flows, but rather, in places where the currents flow both when injected from the left or from the right. A quantitative measure, the harmonic mean of these currents is introduced and correlates very well with the hot spots positions.