Review of Magnetoresistance and Hall Effect in Metals and Semiconductors

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Addis Ababa University


We discuss the theory of transport properties of charged particles in an electric and magnetic fields on aspects relevant to Hall effect and magnetoresistancce. We begin by reviewing magnetic properties of matter in relation to the external applied magnetic field. We show that charged particles moving in a magnetic field follow a curved path because of Lorentz force. When a current carrying conductor is placed in a magnetic field, the charge carriers begin following the curved path in the sample of a conductor until the field is balanced by the Hall field produced. This deflection of electrons from their line of path gives rise to the increase in path length of electrons in the conductor and in turn this reduces the effective current in the conductor. As a result at room temperature and rather low values of magnetic field, resistance of the material increases linearly with the magnetic field strength. And finally we tried to review that at high magnetic fields and low temperatures (about 4 K), the Hall resistance does not increase linearly with the field; instead, the plot showed a series of “stair steps”. The explanation for this effect involves the circular paths in which electrons are forced to move by the field. As the field increases, the orbital radius decreases, permitting more orbits to bunch together on one side of the material. In this regard integer (IQHE) and fractional (FQHE) quantum Hall effects are discussed.



Magnetic Properties, Matter, Magnetoresistance, Hall Effect, Metals, Semiconductors