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Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices
M E Cage1, A Jeffery1, R E Elmquist1
1National Institute of Standards and Technology, Gaithersburg, MD 20899-0001.
Summary
Non-vanishing ac longitudinal resistances significantly affect ac quantized Hall resistance measurements. This study analyzes equivalent circuits to provide corrections for these effects, though frequency dependencies remain unaddressed.
Area of Science:
- Condensed matter physics
- Quantum phenomena
Background:
- Experimental measurements of ac quantized Hall resistance often show significant longitudinal resistances.
- These resistances are observed even when dc longitudinal resistances are negligible under specific temperature and magnetic field conditions.
Purpose of the Study:
- To investigate the impact of non-vanishing ac longitudinal resistances on quantized Hall resistance measurements.
- To analyze the effect using equivalent electrical circuits.
Main Methods:
- Developed equivalent circuits for quantized Hall effect resistors, incorporating additional resistors for longitudinal resistances.
- Simplified circuits by excluding capacitances and inductances.
- Analyzed multi-series connections of quantum Hall effect devices.
Main Results:
- Derived exact algebraic solutions for quantized Hall resistances under finite ac longitudinal resistances.
- These solutions offer corrections to measured quantized Hall resistance values.
Conclusions:
- Finite ac longitudinal resistances necessitate corrections to measured quantized Hall resistances.
- The derived corrections do not explain the frequency-dependent behaviors of ac quantized Hall resistances found in literature.
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