 In other words, the above approach yields zero resistivity whenever the Landau levels are positioned such that the Fermi energy "EF" is in between two levels.Shubnikov-de Haas oscillations can be used to determine the two-dimensional electron density of a sample.For a given magnetic flux formula_7 the maximum number "D" of electrons with spin "S" = 1/2 per Landau level is

Upon insertion of the expressions for the flux quantum and for the magnetic flux relationship () reads
Let "N" denote the maximum number of states per unit area, so and
Now let each Landau level correspond to an edge channel of the above sample.