Review of Classical and Quantum Hall Effect
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Date
2016-02
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Addis Ababa University
Abstract
In this project we review the Classical and Quantum Hall Effects. We discuss these
two effects theoretically based on the available literature. In classical Hall Effect when
a strong magnetic field is applied perpendicular to the electrons plane of movement,
the electrons execute tiny cyclotron orbits around the flux lines. If in addition, an
electric field applied in transverse direction to the induced electric field, the electrons
will tend to drift in a direction perpendicular to both fields, generating the Hall Effect.
For the case of Quantum Hall Effect, energy associated with the cyclotron motion
is quantized giving rise to the Landau levels and at low temperatures all the electrons
are in the lowest Landau level. The filling factor can be changed by varying
the magnetic field B for a fixed carrier density. This leads to the sitation that the
Hall conductivity takes the values equal to e2/h as discussed in Chapter three. The
Quantum Hall Effect can be Integral or Fractional. The Integer Quantum Hall Effect
can be understood in an independent-particle model, without taking into account the
electron-electron interactions, in the Fractional Quantum Hall Effect, where the filling
factors take fractional values (1/2,1/3,1/5,...) the electron-electron interactions play
an essential role. The Coulomb interaction produces incompressible states of highly
correlated carrier motion in high magnetic fields at specific fractional filling levels. At
such magnetic fields the electrons can be treated as quasi particles called composite
fermions
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Quantum Hall Effect