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 ohm standard resistor is of a few parts in 10^8, at present mainly limited by the prototype device and the interferences in the current implementation, with the potential to achieve few parts in 10^9, which is the level of the systematic uncertainty of the quantum Hall Kelvin bridge itself.