Analytical determination of atypical quantized resistances in graphene p-n junctions

A mathematical approach 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 nonconventional, fractional multiples of the typical quantized Hall resistance at the v = 2 plateau (R _H ≈ 12906 Ω) and take the form: $\frac{a}{b}{R}_{\text{H}}$ . 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 devices with multiple source and drain terminals.