Initial NIST AC QHR measurements

Abstract

We demonstrate that dc quantized Hall resistance (dc QHR) guideline properties and dc and ac QHR values can be measured without changing sample probe lead connections at the QHR device, and report ac QHR values that converge to the dc QHR value when using four-terminal-pair ac QHR measurements. This was accomplished during one cooldown using single-series and quadruple-series connections outside the sample probe. The QHR was measured from 0 Hz to 5500 Hz in 1:1 ratio at 20 µA to ±1 part in 107 uncertainties with a poor-quality QHR device. A good device would allow an order of magnitude smaller uncertainties over this frequency range. We exchanged positions of the QHR device and reference resistor in the bridge and remeasured the resistance ratios to remove dominant ac bridge effects.

Hydrodynamic Equations in Quantum Hall Systems at Large Currents

“…A hydrodynamic model 26) has been proposed to explain the observed longitudinal voltage steps. 27,28) It is argued in this model that electron-hole pairs created at inter-Landau-level scatterings near a charged impurity have common features with vortices created when a classical fluid flows past an obstacle. The hydrodynamic equations in the present paper, on the other hand, describe macroscopic spatio-temporal variations, and their typical length scale is much larger than the size of a single electron-hole pair.…”

Quadratic Frequency Dependence of an AC QHR Device

“…So rather than directly compare an ac QHR device with a quadrifilar resistor, we found it easier to compare a quadrifilar resistor with a stable wirewound resistor without having to bother with a superconducting magnet and cyrogens, and then compare that stable wire-wound resistor with an ac QHR device using the magnet. Reference [1] describes those comparisons in detail, demonstrates that all dc QHR guideline properties and all dc and ac QHIR values can be measured in a single cooldown without changing sample probe leads at the device, and shows that quadruple-series-connected ac QHR values measured in the four-terminal-pair mode converge to the dc QHR value. The next section summarizes that experiment.…”

“…This paper deals only with the quadratic dependences. The bridge quadratic dependence is dominant [1] and must be removed. Then either a reference resistor with a calculable quadratic dependence is required to extract its ac-dc difference [2] and thereby determine the quadratic dependence of the ac QHR standard, or the quadratic dependence of the ac QHR standard itself must be determined [3].…”

“…AC quantized Hall resistance (ac QHR) standards have linear and quadratic frequency dependences, as do the reference resistors with which they are compared, and the ac measurement bridges themselves [1]. This paper deals only with the quadratic dependences.…”

Design and development of a coaxial cryogenic probe for precision measurements of the quantum Hall effect in the AC regime

“…The operating conditions can thus be achieved with simpler and less expensive cryogenic systems. Nevertheless, the direct measurement of the quantised resistance in the AC regime requires careful considerations about device wiring and shielding [6]- [8], to minimise the effects of stray parameters which can alter the apparent resistance of the device from the quantised value [7].…”