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Quantum-Hall physics and three dimensions
Johannes Gooth1,2, Stanislaw Galeski1,2, Tobias Meng3
1Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany.
Reports on Progress in Physics. Physical Society (Great Britain)
|February 3, 2023
Summary
The quantum Hall effect (QHE) in 3D materials shows quantized Hall conductivity, similar to 2D systems. Recent experiments clarify the role of QHE physics in three dimensions, settling long-standing questions.
Area of Science:
- Condensed matter physics
- Solid-state physics
- Quantum mechanics
Background:
- The quantum Hall effect (QHE) in 2D electron systems exhibits exact quantization of Hall conductivity.
- Extending QHE phenomena to 3D materials has been a long-standing challenge.
- Previous 3D studies showed similarities but lacked quantitative agreement with QHE theory.
Purpose of the Study:
- To summarize recent advancements in understanding the quantum Hall effect in three dimensions.
- To address the unsettled role of QHE physics in 3D materials.
- To highlight the impact of new experimental findings on the field.
Main Methods:
- Review of recent experimental findings on 3D materials in magnetic fields.
- Analysis of Hall conductivity (σxy) and longitudinal resistivity (ρxx) in 3D systems.
- Comparison of experimental results with theoretical predictions for QHE.
Main Results:
- Recent experiments reveal plateau-like Hall conductivities in 3D materials.
- Minima in longitudinal resistivity are observed, mirroring 2D QHE characteristics.
- New insights into the quantitative relationship between σxy and conductance quantum (e²/hc) in 3D.
Conclusions:
- The quantum Hall effect in 3D is now better understood due to recent experimental breakthroughs.
- These findings clarify the role and manifestation of QHE physics in three-dimensional systems.
- The research signifies a major leap in comprehending 3D matter under magnetic fields.
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