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The Integer QHE & Contact Resistance

The Integer QHE & Contact Resistance. Tim Morgan. Outline. Integer Quantum Hall Effect Quantized Current Density Contact Resistance Energy Barrier. 2-D Electron Systems. Inversion Layer. Gate Voltage & Band Bending. E. Landau Levels. E. y. E F. V g. E. E F. Depletion. z.

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The Integer QHE & Contact Resistance

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  1. The Integer QHE & Contact Resistance Tim Morgan

  2. Outline • Integer Quantum Hall Effect • Quantized Current Density • Contact Resistance • Energy Barrier Tim Morgan | 6.21.05 | UA | IQHE & CR

  3. 2-D Electron Systems Inversion Layer Gate Voltage & Band Bending E Landau Levels E y EF Vg E EF Depletion z Inversion z Translated Cyclic Motion of Electron in Magnetic Field v0 x Tim Morgan | 6.21.05 | UA | IQHE & CR

  4. IQHE Development • Impurities • Electron localization • Delocalization at Landau Levels • Laughlin’s Gedankenexperiment Φ Tim Morgan | 6.21.05 | UA | IQHE & CR

  5. IQHE Considerations & Implications • Conditions that alter the IQHE • Temperature • Large Current • Edges • Conductivity is quantized • Ease in measurement • ρxy = RH • Hall voltage probes placed anywhere on sides 1 2 3 Tim Morgan | 6.21.05 | UA | IQHE & CR

  6. Contact Resistance • Metal-Semiconductor Energy Barrier Tim Morgan | 6.21.05 | UA | IQHE & CR

  7. Summary • 2D Electron Systems • Integer Quantum Hall Effect • Electron Motion  Quantized Energy • Development • Fractional Quantum Hall Effect • Electron Interactions • Odd Integer Fraction Multiples Tim Morgan | 6.21.05 | UA | IQHE & CR

  8. References • D. Yoshioka. The Quantum Hall Effect. Springer. Berlin. 1998. (Diagrams based on images in book.) Tim Morgan | 6.21.05 | UA | IQHE & CR

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