Abstract
Measurement of the Hall effect on a two-dimensional charge carrier system at low temperatures and high magnetic fields leads to the observation of well-defined Hall resistance values which remain constant against variation of the applied magnetic field or the charge carrier density—the quantum Hall effect (QHE). The quantized Hall resistance values depend only on the Planck constant h, the elementary charge e, and either an integer or a fractional valued number. The QHE has enabled in 2019 the redefinition of the International System of Units (SI), based now on five fundamental constants of nature. As described here, the robustness of the QHE is related to the evolution of an electrical compressible/incompressible landscape inside the naturally inhomogeneous charge carrier system with varying magnetic field/charge carrier density. The incompressibility has its origin in the formation of energy gaps, which arise—besides the formation of Landau levels—also by strong correlation effects between the charge carriers.
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