Review of Magnetoresistance and Hall Effect in Metals and Semiconductors
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Date
2017-12-02
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Addis Ababa University
Abstract
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.
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Keywords
Magnetic Properties, Matter, Magnetoresistance, Hall Effect, Metals, Semiconductors