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Integer, fractional, and anomalous quantum Hall effects explained with Eyring's rate process theory and free volume
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Physical Chemistry Chemical Physics : PCCP
|February 14, 2017
Summary
Eyring's rate process theory explains quantum Hall effects, including integer, fractional, and anomalous types. Electron mobility depends on free volume, leading to quantized Hall conductivity in 2D systems.
Area of Science:
- Condensed matter physics
- Quantum mechanics
Background:
- The quantum Hall effects (QHE) describe phenomena in 2D electron systems under strong magnetic fields.
- Existing theories often focus on specific aspects of QHE, necessitating a unified approach.
Purpose of the Study:
- To apply Eyring's rate process theory and the free volume concept to understand various quantum Hall effects.
- To develop a theoretical framework for quantized Hall conductivity applicable to 2D and potentially 3D systems.
Main Methods:
- Utilizing Eyring's absolute rate process theory to model electron conduction as a rate-controlled process.
- Incorporating the free volume concept to describe electron mobility dependence on available space.
- Deriving expressions for Hall conductivity based on these theoretical underpinnings.
Main Results:
- Hall conductivity is shown to be quantized, consistent with experimental observations of integer, fractional, and anomalous QHE.
- Prefactors for quantized Hall conductivity are related to magnetic flux quantum number and magnetic quantum number via the azimuthal quantum number.
- The model provides a unified perspective on Hall effects in both the presence and absence of external magnetic fields.
Conclusions:
- Eyring's rate process theory and free volume concept offer a robust framework for understanding quantum Hall effects.
- The derived quantized Hall conductivity provides a new theoretical perspective on electron transport in 2D systems.
- The theoretical approach is adaptable for extension to three-dimensional systems.
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