The Quantum Hall Effect occurs in two-dimensional electron systems placed under strong magnetic fields at very low temperatures. In this state, the Hall resistance—normally expected to vary smoothly with magnetic field strength—changes in fixed, quantized steps. These steps correspond to precise values that depend only on fundamental physical constants and not on the material itself.
This quantization arises because electrons in the system form discrete energy levels known as Landau levels. As these levels fill up with electrons, the Hall resistance locks into stable plateaus, while the resistance along the direction of current flow drops to zero, indicating nearly perfect, lossless conduction along the edges of the material.
There are two types of quantum Hall effects. The integer quantum Hall effect results from non-interacting electrons filling whole Landau levels. The fractional quantum Hall effect, on the other hand, involves strong interactions between electrons and leads to the emergence of exotic states where particles can carry fractional electric charge.
The Quantum Hall Effect reveals deep connections between quantum physics, electron behavior, and the topological properties of materials.