Review of Classical and Quantum Hall Effect

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Addis Ababa University


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



Quantum Hall Effect