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An ultrastable low-noise current amplifier (ULCA) has been transferred between two laboratories, NPL and PTB, four times, with three of the transfers yielding a relative change in the trans-resistance gain of less than $2 \times 10^{-7}$. This is a new bench-mark for inter-laboratory transfer of small current. We describe in detail the use of a cryogenic current comparator to calibrate the ULCA at NPL, and the use of the ULCA to measure $1$ G$\Omega$ resistors with relative uncertainties at the $10^{-7}$ level., Comment: 8 pages, 7 figures

We performed calibrations of four different commercial picoammeters using the Ultrastable Low-noise Current Amplifier (ULCA) as a calibrator current source operated in the range between 1 femtoampere and 1 microampere. The results allow the comprehensive characterization of the devices under test regarding noise, settling and burden voltage behavior as well as stability of the gain factor, and confirm the performance of the ULCA for use as small-current calibrator standard. Also, we present a further advanced setup for the calibration of transimpedance amplifiers. Accuracy limits for best electrometer calibrations in the current range between 1 femtoampere and 1 microampere and possible implications on corresponding calibration and measurement capabilities are discussed., Comment: 7 pages, 10 figures, 23 references

In the quantum anomalous Hall effect, the edge states of a ferromagnetically doped topological insulator exhibit quantized Hall resistance and dissipationless transport at zero magnetic field. Up to now, however, the resistance was experimentally assessed with standard transport measurement techniques which are difficult to trace to the von-Klitzing constant R$_K$ with high precision. Here, we present a metrologically comprehensive measurement, including a full uncertainty budget, of the resistance quantization of V-doped (Bi,Sb)$_2$Te$_3$ devices without external magnetic field. We established as a new upper limit for a potential deviation of the quantized anomalous Hall resistance from RK a value of 0.26 +- 0.22 ppm, the smallest and most precise value reported to date. This provides another major step towards realization of the zero-field quantum resistance standard which in combination with Josephson effect will provide the universal quantum units standard in the future.

We report on new calibration methods for picoammeters and low-current sources. The "Ultrastable Low-noise Current Amplifier" (ULCA) was used for the exemplary calibration of commercial state-of-the-art ammeter and current source instruments in the current range between 1 femtoampere and 1 microampere. The uncertainties achieved are compared with results obtained from two other calibration methods for small direct currents. It is shown that using the ULCA as calibrator allows achieving lower uncertainties together with the benefit of easier handling compared to alternative techniques. Also, the ULCA allows performing current meter and source calibrations between 1 femtoampere and 1 microampere with a single method., Comment: 2 pages, 1 figure

An interlaboratory comparison of small-current generation and measurement capability is presented with the ultrastable low-noise current amplifier (ULCA) acting as travelling standard. Various measurements at direct currents between 0.16 nA and 13 nA were performed to verify the degree of agreement between the three national metrology institutes involved in the study. Consistency well within one part per million (ppm) was found. Due to harsh environmental conditions during shipment, the ULCA's transfer accuracy had been limited to about +/-0.4 ppm. Supplemental measurements performed at PTB indicate that further improvements in accuracy are possible. Relative uncertainties of 0.1 ppm are achieved by applying on-site calibration of the ULCA with a suitable cryogenic current comparator., Comment: 13 pages, 8 figures

We report on high-accuracy measurements of quantized current, sourced by a tunable-barrier single-electron pump at frequencies $f$ up to $1$ GHz. The measurements were performed with a new picoammeter instrument, traceable to the Josephson and quantum Hall effects. Current quantization according to $I=ef$ with $e$ the elementary charge was confirmed at $f=545$ MHz with a total relative uncertainty of 0.2 ppm, improving the state of the art by about a factor of 5. For the first time, the accuracy of a possible future quantum current standard based on single-electron transport was experimentally validated to be better than the best realization of the ampere within the present SI.

An ultrastable low-noise current amplifier (ULCA) is presented. The ULCA is a non-cryogenic instrument based on specially designed operational amplifiers and resistor networks. It involves two stages, the first providing a 1000-fold current gain and the second performing a current-to-voltage conversion via an internal 1 MOhm reference resistor or, optionally, an external standard resistor. The ULCA's transfer coefficient is extremely stable versus time, temperature and current amplitude within the full dynamic range of +/-5 nA. A low noise level of 2.4 fA/sqrt(Hz) helps to keep averaging times low at small input currents. A cryogenic current comparator is used to calibrate both input current gain and output transresistance, providing traceability to the quantum Hall effect. Typically, within one day after calibration, the uncertainty contribution from short-term fluctuations of the transresistance is below one part in 10^7. The long-term stability is expected to be better than one part in 10^5 over a year. A high-precision variant is available that shows a substantially improved stability at the expense of a higher noise level of 7.5 fA/sqrt(Hz). The ULCA also allows the traceable generation of small electrical currents or the calibration of high-ohmic resistors., Comment: 28 pages, 21 figures

A standard method for picoammeter calibrations is the capacitor charging technique, which allows generating traceable currents in the sub-nA range. However, its accuracy is limited by the ac-dc differences of the capacitances involved. The Ultrastable Low-noise Current Amplifier (ULCA) is a novel high-precision amperemeter for direct current measurements in the pA range, developed at PTB. Its amplifier stages, based on resistor networks and op-amps, can be calibrated traceably with a cryogenic current comparator (CCC) system. We compare the results from both independent calibration routes for two different ULCA prototypes. We find agreement between both methods at an uncertainty level below 10 microA/A, limited by the uncertainty of the currents generated with the capacitor charging method. The investigations confirm the superior performance of the new ULCA picoammeter., Comment: 8 pages, 3 figures

We present the comparison of results from the generation and the measurement of direct currents in the pA range, performed with traceable state-of-the-art methods at highest accuracy. The currents were generated with the capacitor charging method, and measured with the first prototype of a novel picoammeter developed at PTB. The results confirm the agreement between both methods and the linearity of the new picoammeter at an uncertainty level of few microA/A. Also, they shed light on the ac-dc difference of capacitors, crucial for current generation with the capacitor charging method., Comment: 2 pages, 1 figure. Contribution (summary paper, to appear in IEEE CPEM 2014 Conference Digest) accepted for presentation on the Conference on Precision Electromagnetic Measurements (CPEM) 2014 in Rio de Janeiro (Brazil), 24-29 August 2014

Quantum Metrology Triangle experiments combine three quantum electrical effects (the Josephson effect, the quantum Hall effect and the single-electron transport effect) used in metrology. These experiments allow important fundamental consistency tests on the validity of commonly assumed relations between fundamental constants of nature and the quantum electrical effects. This paper reviews the history, results and the present status and perspectives of Quantum Metrology Triangle experiments. It also reflects on the possible implications of results for the knowledge on fundamental constants and the quantum electrical effects., Comment: 36 pages, 8 figures

The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 10^7. This paper reports the considerable progress recently achieved with a new generation of single-electron tunnelling devices. A five-junction R-pump was operated with a relative charge transfer error of five electrons in 10^7, and was used to successfully perform single-electron charging of a cryogenic capacitor. The preliminary result for the single-electron charge quantum has an uncertainty of less than two parts in 10^6 and is consistent with the value of the elementary charge., Comment: 16 pages, 9 figures, 1 table

A reliable process has been developed for the fabrication of all-Nb single-electron circuits, based on spin-on glass planarization. The process steps are the in situ growth of Nb/AlOx/Nb sandwich, definition of the patterns of junctions, base electrodes and wiring by use of reactive ion etching and the planarization of a spin-on glass insulation between base electrode and wiring. A single electron transistor made of 0.1 square micrometer area junctions clearly shows the e-periodic Coulomb blockade modulation by a voltage applied to a gate., Comment: 3 pages, 4 figures