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Published on: January 21, 2016
Fundamental relation between longitudinal and transverse conductivities in the quantum Hall system
Akira Endo1, Naomichi Hatano, Hiroaki Nakamura
1Institute for Solid State Physics, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8581, Japan.
Summary
We found a proportional relationship between conductivity tensor components in quantum Hall systems. This finding quantitatively matches experimental data from GaAs/AlGaAs, offering insights into electron behavior under magnetic fields.
Area of Science:
- Condensed Matter Physics
- Quantum Hall Effect
- Solid State Physics
Background:
- The quantum Hall effect (QHE) describes phenomena in 2D electron systems subjected to strong magnetic fields.
- Understanding the conductivity tensor components (σ(xx) and σ(xy)) is crucial for QHE.
- Disorder and impurity potentials significantly influence Landau level broadening.
Purpose of the Study:
- To investigate the relationship between diagonal (σ(xx)) and off-diagonal (σ(xy)) conductivity tensor components.
- To develop an analytical model for these components under specific approximations.
- To compare theoretical predictions with experimental results in GaAs/AlGaAs systems.
Main Methods:
- Linear response theory was employed to calculate conductivity components.
- An approximation was used, replacing self-energy with a constant scattering time (τ).
- This approximation models Landau level broadening as a Lorentzian function.
Main Results:
- Analytic formulas for σ(xx) and σ(xy) were derived at low temperatures.
- A proportional relation was found: dσ(xy)/dB ∝ Bσ(xx)(2).
- The derived relation showed quantitative agreement with experimental data in GaAs/AlGaAs.
Conclusions:
- The study establishes a key relationship between conductivity tensor components in QHE.
- The simplified model provides a good approximation for experimental observations.
- This work contributes to understanding electron dynamics in 2D systems under magnetic fields.
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