Historical Context and Outlook of Quantum Hall Research for the Redefined SI

Abstract

To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many interesting quantum phenomena. The QHE may be exhibited by a 2D electron system when placed under a strong magnetic field perpendicular to the plane of the system. These conditions allow for Landau quantization, or the discretization of available energies of the electrons affected by the magnetic field. These energy values, determined by solving the Schr\"odinger equation, are known as Landau levels. During the course of a QHE measurement, one defines the Hall resistance Rxy as the measured voltage, perpendicular to the direction of the applied current, divided by that same current. The characteristic longitudinal resistivity \r{ho}xx goes to zero as Rxy approaches a quantized value (nominally called a plateau).