چكيده به لاتين
Abstract:
The experimental results of the classical Hall effect show that the transverse resistance or the "Hall resistance" increases linearly with the magnetic field while the longitudinal resistance is constant. The classical Hall effect was the first experiment to show that electric currents in metals exist due to the flow of electric charge and not to the flow of protons.
In an experiment subjected to low temperature and high magnetic field in order to observe the integer quantum Hall effect, it was shown that the transversal resistance of a two-dimensional electron gas system doesn't change linearly w.r.t to a magnetic field, in the same manner, it does in the classical Hall effect. Otherwise, it has shown that different Hall plateaus were associated with discrete magnitudes of the magnetic field applied. The reason behind the emergence of those quantum plateaus is that the filling factor of Landau levels is an integer. If Landau levels were partially filled, the filling factor would be a fractional number and a fractional quantum Hall effect would otherwise form. Hall effect is very useful for indicating the polarity of electric charges and for determining physical constants.
An experiment that was demonstrated to observe the spin quantum Hall effect in the quantum well HgTe of inverse band structure showed that the spin quantum Hall effect, in contrast to the quantum Hall effect can be obtained even with the absence of magnetic field, as we have bands that carry spin current, not charge currents. In this case, by applying an electric field, the spin-up and spin-down states move in different one-dimensional independent channels and generate discrete Hall conduction.
The spin quantum Hall effect plays an important role in the field of spintronics. By making some research we conclude that the difference between quantum Hall effect in graphene and two-dimensional systems, especially the "ultra-relativistic" system, is that the low energy carriers are present in graphene and they can be analyzed using the Dirac equation. On the other hand, the electrons can be studied using the non-relativistic Shroedinger equation. Experiments showed that quantum plateaus in graphene with one layer, two-layers, and three layers get obtained with different filling factors.
