Quantum Hall Effect Devices Research Articles

Quantum Hall effect devices as circuit elements

The electrical behaviour of a quantum Hall effect device is described in terms of an equivalent circuit. This circuit is able to model the principal electrical characteristics of an ungated Hall bridge device. The effects of electrical loading of the Hall terminals and some anomalous effects related to contact resistances are investigated experimentally using a GaAs/AlGaAs modulation-doped device and are described in terms of the equivalent circuit.

A Test of the Quantum Hall Effect as a Resistance Standard

This paper demonstrates that the quantum Hall effect can be used to monitor a laboratory unit of resistance. A 6453.2-Ω room temperature reference resistor was calibrated relative to two quantum Hall effect devices with a 0.017-ppm (1 σ) uncertainty for each 1 h measurement period. This accuracy was achieved by correcting for a measurement system offset error and for the temperature dependences of each quantum Hall device. Hamon series-parallel resistor networks were then used to calibrate the 6453.2-Ω resistor in terms of the five one ohm resistors which comprise the NBS ohm. The total lΩ accuracy for the transfer between the quantum Hall devices and the 1-Ω resistors was 0.047 ppm.

Implications of the chiral anomaly for quantum Hall-effect devices.

The anomaly equation ${\ensuremath{\partial}}_{\ensuremath{\mu}}$${J}_{5}$${}^{\ensuremath{\mu}}$=-(${e}^{2}$/8${\ensuremath{\pi}}^{2}$ ${\ensuremath{\Elzxh}}^{2}$c) (${F}_{\ensuremath{\lambda}\ensuremath{\sigma}}^{\mathrm{*}}$${F}^{\ensuremath{\lambda}\ensuremath{\sigma}}$) is used to derive a relationship between the filling factor (\ensuremath{\nu}) and the Hall conductance on the gate capacitor of a field-effect-transistor device. In addition, the chiral phase (\ensuremath{\theta}) states are shown to be related to those of the filling factor by \ensuremath{\Vert}\ensuremath{\theta}〉=\ensuremath{\Vert}2\ensuremath{\pi}\ensuremath{\nu}〉. .AE