Fermi energy
The result of zero resistivity between the contacts 2 and 3 is a consequence of the electrons being mobile only in the edge channels of the sample. The situation would be different if a Landau level came close to the Fermi energy "E"F. Any electrons in that level would become mobile as their energy approaches the Fermi energy "E"F. Consequently, scatter would lead to "R"SdH &gt; 0. In other words, the above approach yields zero resistivity whenever the Landau levels are positioned such that the Fermi energy "E"F is in between two levels.