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Quantum Hall Effect

Brief analysis of quantum Hall effect and calculation of quantum Hall resistance

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Quantum Hall Effect

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  1. Course: Quantum Electronics Arpan Deyasi Quantum Topic: Quantum Hall Effect Electronics Arpan Deyasi Arpan Deyasi, RCCIIT, India 5/10/2020 1

  2. What is Q.H.E? Arpan Deyasi It is a phenomenon where resistance of a quantum well system is quantized under the condition of low temperature and high magnetic field Electronics Quantum 5/10/2020 Arpan Deyasi, RCCIIT, India 2

  3. Calculation of Quantum Hall Resistance Arpan Deyasi 2 Energy of quantum well system Quantum 2 2 = + *( ) E k k y z 2 m No. of energy states per energy interval in real space Electronics 1  2 2 ( )  = + ( ) N k k y z 2 5/10/2020 Arpan Deyasi, RCCIIT, India 3

  4. Calculation of Quantum Hall Resistance Arpan Deyasi Density of states of any quantum well system for a particular subband Quantum Electronics * m  = ( ) E  2 5/10/2020 Arpan Deyasi, RCCIIT, India 4

  5. Calculation of Quantum Hall Resistance Arpan Deyasi K.E in magnetic field is quantized upto Landau level because of cyclotron motion Quantum Energy separation between two Landau level is Electronics  c qB m  = where c * cyclotron motion 5/10/2020 Arpan Deyasi, RCCIIT, India 5

  6. Calculation of Quantum Hall Resistance Arpan Deyasi No. of energy states upto Landau level Quantum =   ( ) E N L c Electronics * m qB m = N L  2 * qB  = N L 5/10/2020 Arpan Deyasi, RCCIIT, India 6

  7. Calculation of Quantum Hall Resistance Arpan Deyasi Quantum Hall Resistance Quantum B = R QH qN L Electronics  B q =  R QH qB h q = R QH 2 2 5/10/2020 Arpan Deyasi, RCCIIT, India 7

  8. Significance of Quantum Hall Resistance Arpan Deyasi Quantum Hall Resistance is constant Quantum h = R QH 2 iq Electronics 5/10/2020 Arpan Deyasi, RCCIIT, India 8

  9. Significance of Quantum Hall Resistance Arpan Deyasi Landau level below Fermi level are completely filled and above are completely empty Quantum Due to existence of impurity and disorder, sharp Landau levels become broader Electronics Landau levels with broader width are called Landau band 5/10/2020 Arpan Deyasi, RCCIIT, India 9

  10. Significance of Quantum Hall Resistance Arpan Deyasi Carriers at tail of Landau band are localized at lower temperature, which don’t contribute to electrical conduction Quantum Therefore, if Fermi level lies in localized state, Hall resistance remains constant Electronics 5/10/2020 Arpan Deyasi, RCCIIT, India 10

  11. References Arpan Deyasi https://physics.stackexchange.com/questions/476184/quantum-hall-effect- why-the-spikes-of-the-longitudinal-resistance-appear-every Quantum Electronics 5/10/2020 Arpan Deyasi, RCCIIT, India 11

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