Cascaded quantum hall bisection and applications to quantum metrology

We demonstrate a programmable quantum Hall circuit that implements an iterative voltage bisection scheme and allows any binary fraction (k/2n) of the fundamental resistance quantum RK/2=h/2e2 to be obtained. The circuit requires a number n of bisection stages that only scales logarithmically with the resolution of the set of possible output fractions. The value of k can be set to any integer between 1 and 2n by proper and easily predictable gate configuration. The architecture exploits gate-controlled routing, mixing, and equilibration of edge modes of robust quantum Hall states. The device does not contain internal Ohmic contacts and is thus naturally robust towards stray-resistance effects. Our scheme offers an alternative way to obtain custom quantum Hall resistance standards, and its potential advantages are discussed. The basic viability of the approach is demonstrated in a proof-of-principle two-stage bisection circuit built on a high-mobility GaAs/(Al,Ga)As heterostructure operating at a temperature of 260mK and a magnetic field of 4.1T. Our prototype achieves a relative quantization precision of the order of 10-4, which is limited by the experimental setup rather than by the circuit itself.