Implementation of a graphene quantum Hall Kelvin bridge-on-a-chip for resistance calibrations

The unique properties of the quantum Hall effect allow one to revisit traditional measurement circuits with a new flavour. In this paper we present the first realization of a quantum Hall Kelvin bridge for the calibration of standard resistors directly against the quantum Hall resistance. The bridge design is particularly simple and requires a minimal number of instruments. The implementation here proposed is based on the bridge-on-a-chip, an integrated circuit composed of three graphene quantum Hall elements and superconducting wiring. The accuracy achieved in the calibration of a 12 906 standard resistor is of a few parts in 108, at present mainly limited by the prototype device and the interferences in the current implementation, with the potential to achieve few parts in 109, which is the level of the systematic uncertainty of the quantum Hall Kelvin bridge itself.