The Quantum Hall Effect is a remarkable phenomenon where the electrical conductivity of a two-dimensional electron system becomes quantized—meaning it takes on exact, discrete values rather than varying continuously.
Discovered in 1980 by Klaus von Klitzing, this effect occurs when electrons are confined to a very thin layer (essentially two-dimensional), cooled to near absolute zero, and subjected to a strong perpendicular magnetic field. Under these conditions, the Hall resistance (a measure of voltage produced across the sample due to an applied current and magnetic field) doesn’t vary smoothly. Instead, it jumps in precise steps, with values given by:
R = h / (e² × n)
Here, h is Planck’s constant, e is the elementary charge, and n is an integer. These steps are incredibly accurate and universal, unaffected by the material’s shape, impurities, or other details. This makes the quantum Hall effect a gold standard for measuring resistance in metrology.
The effect arises due to the formation of Landau levels—quantized energy levels that electrons occupy in a magnetic field—and the unique behavior of edge currents in 2D systems. It’s a striking demonstration of how quantum mechanics can govern the collective behavior of particles on macroscopic scales.
A variant, the fractional quantum Hall effect, discovered later, shows even more exotic behavior involving quasi-particles with fractional electric charge, deepening our understanding of quantum states and topological phases of matter.