In two-dimensional electron gas when a large magnetic field is applied in one direction and an electric field perpendicular to it, there is a current in a direction perpendicular to both. This current is called the Hall effect. It remained without
quantization until 1980 when it was found that the quantization leads to correct measurement of h/e2 . Therefore, the quantized Hall
effect was further studied at high magnetic fields where
fractional quantization was found. The fractional
charge can arise from the "incompressibility" in the flux quantization. Laughlin wrote a wave function, the excitations of which are fractionally charged quasiparticles. This wave
function comes in competition with charge density waves but for a few fractions it does give the ground state. If "incompressibility" is not considered and it is allowed to be compressible, the fractional charge can arise from the angular momentum which appears in the Bohr magneton in the form of g values. Usually the positive
spin is considered but we consider both the positive as well as the negative
values so that there is a spin-charge coupling. The values thus calculated for the fractional charge agree with the experimental data on the quantized Hall effect. We have followed this subject for a long time and have reviewed the subject.
More abstracts about the The quantum Hall effect: Spin-charge locking