A geometric explanation of the temperature dependence of the quantised Hall resistance

Abstract

An explanation is given of the temperature dependence of the quantised Hall resistance RH for temperatures below 4 K. In the measured RH a certain fraction of the longitudinal resistivity rho xx enters through two independent mechanisms, both amounting to an effective Hall probe misalignment. The first one is based on obliqueness of the current flow through the two-dimensional channel, whereas the second one is due to the width of the Hall probes. These mechanisms justify the practice of extrapolating RH(Rx) curves to Rx=0 in order to obtain a zero-temperature value of the quantised Hall resistance.