Adjusting the losses in an ac quantum Hall sample

Abstract

The ac quantum Hall resistance measured with frequencies in the range of a few kilohertz shows characteristic deviations from the dc quantum Hall resistance. These deviations indicate ac losses which increase linearly with frequency. To investigate these losses, a Hall bar with an inner and an outer "window" has been tested. When external voltages are supplied to the windows, the ac losses can be adjusted to zero. This is explained by a phenomenological model for the current distribution in the Hall bar and leads to a model for the ac losses.

Compendium for precise ac measurements of the quantum Hall resistance

“…The presence of gates driven at an ac voltage U G (or of any conductor at shield potential close to the device) modifies the frequency-and current-coefficients in a way which can be described by factors λ . These factors describe how much the capacitive loading of the QHR device is reduced by biasing the capacitances of the QHR device with the external electric gate field [7]. This will be further discussed in section 5.2.…”

“…Another reason for this progress was an improved understanding of the effect of gates [6][7][8]. In general, a gate, and other conductors close to the QHE device, act as parasitic capacitive electrodes and increase the frequency-and current-dependent effects [8].…”

“…= distance between potential contacts g = superposition of R xx0 if R xy is measured at non-opposing potential contacts (21) As argued in [6,7], the capacitive effects occur mainly in the edge regions of the QHE device.…”

“…After the first precision ac measurement of the QHR had demonstrated an accuracy of a few parts in 10 6 [4], considerable progress has been made on the subject of accurate ac QHR measurements [5][6][7][8][9][10][11][12][13][14][15]. Today, measurements with carefully set up ac bridges achieve an uncertainty of a few parts in 10 8 , and agreement at this level has been achieved between different NMIs.…”

Initial NIST AC QHR measurements

“…An important step in developing the ac quantized Hall resistance (ac QHR) [ 1 – 10 ] as an intrinsic impedance standard based on the dc QHR [ 11 – 13 ] is to measure the dc QHR guideline properties [ 14 ] and the dc and ac QHR values without changing sample probe lead contacts at the QHR device. (Otherwise guideline properties should be remeasured.)…”