Quantum hall effects in two-dimensional electron systems: a global approach

Up to almost the last two decades all the experimental results concerning the quantum Hall effect (QHE), i.e. the observation of plateaux at integer or fractional (FQHE) values of the constant h/e(2), were related to quantum-wells in semiconductor heterostructures. However, more recently, a renewed interest in revisiting these phenomena has arisen thanks to the observation of entirely similar effects in graphene and topological insulators. In this paper we show an approach encompassing all these QHEs using the same theoretical frame, entailing both Hall effect plateaux and Shubnikov-de Haas oscillations. Moreover, the model also enables the analysis of both phenomena as a function not only of the magnetic field but the gate voltage as well. More specifically, in the light of the approach, the FQHE in any two-dimensional electron system appears to be an effect of the breaking of the degeneration of every Landau level, n, as a result of the electrostatic interaction involved, and being characterized by the set of three integer numbers (n, p, q), where p and q have clear physical meanings too.