KvanttiHallilmiö

KvanttiHallilmiö is a quantum mechanical phenomenon observed in two-dimensional electron systems subjected to a strong perpendicular magnetic field and low temperatures. When a current flows through such a system, a voltage develops perpendicular to both the current and the magnetic field. In the classical Hall effect, this voltage is proportional to the current and magnetic field strength. However, in the kvanttiHallilmiö, the Hall resistance, which is the ratio of the transverse voltage to the current, is quantized into discrete, universal values.

These quantized values are given by $R_H = \frac{h}{ie^2}$, where $h$ is Planck's constant, $e$ is the elementary charge, and $i$ is an integer. This phenomenon signifies a profound transition from classical to quantum behavior in condensed matter physics. The remarkable precision of these quantized resistance plateaus makes the kvanttiHallilmiö a fundamental standard for electrical resistance.

The phenomenon is understood through the formation of Landau levels, which are discrete energy levels that electrons occupy in a magnetic field. In the kvanttiHallilmiö regime, the Fermi level lies within an energy gap between Landau levels, leading to a suppression of scattering and the formation of robust, dissipationless edge states. These edge states carry the current along the boundaries of the 2D system.

There are two main varieties: the integer kvanttiHallilmiö, where $i$ is an integer, and the fractional kvanttiHallilmiö, where $i$ is a fraction. The fractional effect, discovered later, is attributed to electron-electron interactions and the formation of exotic quasiparticles with fractional charge. The kvanttiHallilmiö has had a significant impact on fundamental physics research and metrology.