An approach to the QHE in 3D electron systems

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• The integer quantum Hall effect (IQHE) is well-understood in 2D systems like graphene.
• Extending this understanding to 3D electron systems remains a challenge.
• Previous models focused on 2D electron behavior.

Purpose of the Study:

• To develop a theoretical framework for the 3D IQHE.
• To generalize existing 2D models to 3D semimetals.
• To explain quantized Hall conductivity in 3D systems.

Main Methods:

• Generalization of a single-electron approach from 2D to 3D systems.
• Application of the Poisson summation method to derive the density of states.
• Incorporation of Landau quantization, Gaussian broadening, spin splitting, and thermal damping.

Main Results:

• A theoretical model for 3D IQHE in semimetals.
• The model reproduces Shubnikov-de Haas oscillations and quantized Hall conductivities.
• Hall conductivity is quantized proportionally to [Formula: see text], matching experimental findings.

Conclusions:

• The proposed framework offers a unified description of quantum magnetotransport across dimensions.
• Key parameters governing 3D IQHE in semimetals are identified.
• The model provides insights into 3D quantum Hall states.