In a typical Hall effect setup, a current is passed through a two-dimensional electron gas (2DEG), and a perpendicular magnetic field is applied. The electrons experience a Lorentz force, causing them to accumulate on one side of the material, creating a transverse voltage known as the Hall voltage. In the quantum regime, the Hall resistance becomes quantized, taking on values of \( R_H = \frac{h}{e^2 \nu} \), where \( h \) is Planck's constant, \( e \) is the electron charge, and \( \nu \) is the filling factor, an integer. This quantization is extraordinarily precise and robust against perturbations, making it useful for metrology.
