quantum Hall effecteffect
Discovered by Klaus von Klitzing in 1980, the integer quantum Hall effect showed that the Hall resistance of a two-dimensional electron gas in a perpendicular magnetic field is quantized: R_H = h/(ν e²), where ν = 1,2,3,... This is a universal phenomenon, independent of the sample material. In 1982, in cleaner samples, the fractional quantum Hall effect was discovered, where ν is a rational number with an odd denominator, explained by the formation of composite fermions — quasiparticles combining electrons with an even number of magnetic flux vortices.
How it works
In practice, it is used for ultra-precise determination of fundamental constants and as a resistive standard. The effect itself is a window into topological phases of matter.
💡 The quantization accuracy is so high that the von Klitzing constant R_K = 25812.80745... Ω is used to establish a new definition of the kilogram via the Planck constant.
\sigma_{xy} = \nu \frac{e^2}{h}
σ_xy — Hall conductivity (inverse Hall resistance, in Ω⁻¹), ν — Landau level filling factor (dimensionless number, ν = N_e / N_Φ, where N_e is the number of electrons, N_Φ is the number of magnetic flux quanta), e — elementary charge (e ≈ 1.602×10⁻¹⁹ C), h — Planck constant (h ≈ 6.62607015×10⁻³⁴ J·s). Hence the Hall resistance R_H = h/(ν e²) = R_K/ν, where R_K is the von Klitzing constant, R_K ≈ 25812.80745 Ω.