The quantum Hall effect: spin-charge locking

Abstract

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 quantum Hall effect. We have followed this subject for a long time and hence have reviewed the subject. There are several interesting concepts which we learn from this subject. The concept of the Hall effect is quite clear particularly when combined with the flux quantization. We learn about the Landau levels and hence the boson character of electrons in two dimensions. We learn that charge becomes a vector quantity and there is spincharge coupling.