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Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices



Marvin E. Cage, Anne-Marie Jeffery, Randolph Elmquist, Kevin C. Lee


Many ac quantized Hall resistance experiments have measured significant values of ac longitudinal resistances under temperature and magnetic field conditions in which the dc longitudinal resistance values were negligible. We investigate the effect of non-vanishing ac longitudinal resistances on measurements of the quanitzed Hall resistances by analyzing equivalent circuits of quantized Hall effect resistors. These circuits are based on ones reported previously for dc quantized Hall resistors, but use additional resistors to represent longitudinal resistances. For simplification, no capacitances or inductances are included in the circuits. The analysis is performed for many combinations of multi-series connections to quantum Hall effect devices. The exact algebraic solutions for the quantized Hall resistances under these conditions of finite ac longitudinal resistances provide corrections to the measured quantized Hall resistances, but these corrections do not account for the frequency dependences of the ac quantized Hall resistances reported in the literature.
Journal of Research (NIST JRES) -


ac quantum Hall effect, equivalent electrical circuit, longitudinal resistance, multi-series connections, quantized Hall resistance


Cage, M. , Jeffery, A. , Elmquist, R. and Lee, K. (1998), Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed June 20, 2024)


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Created October 31, 1998, Updated October 12, 2021