Potential and Current Distributions Calculated Across a Quantum Hall Effect Sample at Low and High Currents.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics

Background:

• The quantum Hall effect (QHE) is a phenomenon observed in two-dimensional electron systems subjected to strong magnetic fields.
• Understanding potential and current distributions is crucial for characterizing QHE devices.

Purpose of the Study:

• To calculate potential and current distributions across a QHE sample width for varying applied currents.
• To incorporate both confining and current-induced charge-redistribution potentials for a more accurate model.

Main Methods:

• Developed a model using parabolic confining potential and logarithmic charge-redistribution potential.
• Determined potential parameters from existing experimental data (localization and breakdown experiments).
• Calculated unique potential distributions for currents from 0 μA to 225 μA.

Main Results:

• The combined potential model yields unique solutions for each current.
• Demonstrated realistic spatial extent of the conducting two-dimensional electron gas.
• Observed current cut-off at sample edges, e.g., no flow within 55 magnetic lengths for currents < 215 μA.
• Achieved excellent agreement between calculated and contactless electro-optic measurements.

Conclusions:

• The novel potential model accurately describes current flow in QHE samples.
• The findings provide a more refined understanding of charge distribution and transport phenomena in QHE systems.
• Experimental validation confirms the model's predictive power for quantum Hall effect devices.