A heuristic quantum theory of the integer quantum Hall effect

Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the quantum current through a Hall device that does not invoke disorder or interactions as the cause of the integer quantum Hall effect (QHE), but is based on a proper quantization of the classical electron drift motion. The theory yields a quantitative description of the breakdown of the QHE at high current densities that is in agreement with experimental data. Furthermore, several of its key points are in line with recent findings of experiments that address the dependency of the QHE on the 2DEG bias voltage, results that are not easily explained within the framework of conventional QHE models. PACS: 73.43.Cd: Quantum Hall effects: Theory and modeling 1 Open problems in the quantum Hall effect. Despite more than 25 years of effort to understand the nature of the quantum Hall effect (QHE), no comprehensive theoretical description emerged that is unanimously accepted. For instance, von Klitzing et. al recently remarked: “[The edge-channel model of Büttiker] is widely used in textbooks on the integer QHE. We don’t want to discuss it here, since recent experimental observations of the current distribution point to a somewhat different microscopic picture of the QHE.” ([1], p. 41. Translation by the author, the experiment Klitzing refers to is [30]). Unsolved problems remain, in particular the origin of the breakdown of the QHE at high current densities and thus large electric Hall fields.