High-accuracy graphene quantum Hall array resistance standards based on wye-delta transformation

Abstract The wye-delta (Y-∆) transformation has been demonstrated to significantly reduce the number of Hall bars necessary for high-resistance quantum Hall array resistance standards (QHARS), addressing the spatial limitation in the practical applications. Network designs have been described for graphene-based Y-∆ arrays to realize resistance values of $$77\frac{h}{2{e}^{2}}$$ 77 h 2 e 2 ( ≈ 1 MΩ), $$775\frac{h}{2{e}^{2}}$$ 775 h 2 e 2 ( ≈ 10 MΩ), and $$7748\frac{h}{2{e}^{2}}$$ 7748 h 2 e 2 ( ≈ 100 MΩ). A programmable QHARS is conceived based on a Y-network with multiple arms. We will present the magnetoresistance transport properties of Y-∆ array devices, followed by the precision measurements of three identical devices, each consisting of 28 Hall bars. At 1.6 K, two devices are quantized at $$77\frac{h}{2{e}^{2}}$$ 77 h 2 e 2 ( ≈ 1 MΩ) to within 80 nΩ/Ω at magnetic field as low as 5 T and 6 T, respectively. Such high accuracy is achieved without cryogenic current comparator, but through a solution that utelizes the triple-connections to the three terminals of the Y-∆ array device, a dual-source bridge (DSB), and a substitution method. Our results establish the viability of a LHe-free quantum Hall resistance (QHR) system with accuracy of a few parts in 10 8 for high-resistance calibration. This system is readily adoptable to improve traceability and reduce the calibration chain for industrial applications.