Quantum Hall state

A quantum Hall state is a two-dimensional electronic state exhibiting quantized transverse transport in a strong perpendicular magnetic field. In an ideal plateau regime, the longitudinal conductivity is suppressed while the Hall conductivity takes ${\sigma }_{xy}=\nu e^2/h$. Integer and fractional values of the filling-related label $\nu$ distinguish different regimes.

Landau levels organize the single-particle spectrum, while interactions are essential to fractional states. A measured plateau reflects a robust bulk response together with the role of edges and disorder; it is not obtained simply by replacing a classical carrier density with an integer in the ordinary Hall formula.