Collapse of the Quantised Hall Resistance and Role of the Diagonal Resistivity in the Quantum Hall Effect

Abstract

Collapse of the quantized Hall resistance (QHR) R_H(4) in high precision and change in the diagonal resistivity ρ_xx with the increase in source–drain current I_SD are measured in GaAs/AlGaAs heterostructure Hall bars used for the confirmation of the sample-width independent accuracy of the R_H(i) (i: an integer) by Jeanneret et al. [IEEE Trans. Instrum. Meas. 44 (1995) 254]. Compared with our butterfly-type Hall bars, the Jeanneret-type Hall bars show the same behavior in the collapse of the QHR while the change in ρ_xx against I_SD shows significantly different behavior. Jeanneret-type Hall bars appear to show more homogeneous electronic properties than butterfly-type Hall bars. Effect of structures of the central narrow channel and voltage probes for ρ_xx and R_H measurement in both Hall bars and correlation between the deviation of the Hall resistance ΔR_H=R_H−R_H(4) and ρ_xx with the increase in I_SD are discussed.