Algorithm for constructing customized quantized resistances in graphene $p-n$ junctions

An algorithm is introduced for predicting quantized resistances in graphene p-n junction devices that utilize more than a single entry and exit point for electron flow. Depending on the configuration of an arbitrary number of terminals, electrical measurements yield fractional multiples of the typical quantized Hall resistance at the $\nu =2$ plateau $R_H\approx 12906\mathrm{\Omega }$ and take the form: $\frac{a}{b}{R}_H$. This theoretical formulation is independent of material, and applications to other material systems that exhibit quantum Hall behaviors are to be expected. Furthermore, this formulation is supported with experimental data from graphene-based devices with multiple source and drain terminals.