Cascaded Quantum Hall Bisection and Applications to Quantum Metrology

Abstract

We demonstrate a programmable quantum Hall circuit that implements a novel iterative voltage bisection scheme and allows obtaining any binary fraction $(k/2^n)$ of the fundamental resistance quantum $R_K/2=h/2e^2$. The circuit requires a number $n$ of bisection stages that only scales logarithmically with the precision of the fraction. The value of $k$ can be set to any integer between 1 and $2^n$ by proper gate configuration. The architecture exploits gate-controlled routing, mixing and equilibration of edge modes of robust quantum Hall states. The device does not contain {\em any} internal ohmic contact potentially leading to spurious voltage drops. Our scheme addresses key critical aspects of quantum Hall arrays of resistance standards, which are today widely studied and used to create custom calibration resistances. The approach is demonstrated in a proof-of-principle two-stage bisection circuit built on a high-mobility GaAs/AlGaAs heterostructure operating at a temperature of $260\,{\rm mK}$ and a magnetic field of $4.1\,{\rm T}$.