The Quantum Hall Effect consists on the gradual behaviour of Hall resistance when it varies the intensity of the magnetic field applied to systems that have a high density of electrons confined in two dimensions and are exposed to very low temperatures. One of the main challenges of Condensed Matter Physics has been explaining the existence, height and wide of these anomalous steps, in the last twenty years. Although there is today a theory that allows understanding the essential aspects of this phenomenon, there is not a solution derived directly from quantum mechanics movement equations, subsisting polemic points and gaps in the detailed qualitative description of the properties of systems of quantum Hall effect regime.

The authors present two significant contributions to the construction of a basic theory of effect. The first theory consists on obtaining and evaluating exact solutions of the movement equations in the approach of middle field for filling factors with Landau levels similar to 1/2 and 1/3. With these, it is estimated the correlation energy, which allows refuting previous arguments that discarded this type of solutions as alternatives for the description of minor energy states of the system. The second contribution is the quantitative description of the list of impurities and crystalline defects in the formation and width of Hall resistance steps that characterize the effect.

These results have been published in five articles in prestigious magazines and presented in two high-level international events in this subject.