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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: 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 devices with multiple source and drain terminals.

Homogeneous, single-crystal, monolayer epitaxial graphene (EG) is the one of most promising candidates for the advancement of quantized Hall resistance (QHR) standards. A remaining challenge for the electrical characterization of EG-based quantum Hall devices as a useful tool for metrology is that they are electrically unstable when exposed to air due to the adsorption of and interaction with atmospheric molecular dopants. The resulting changes in the charge carrier density become apparent by variations in the surface conductivity, the charge carrier mobility, and may result in a transition from n-type to p-type conductivity. This work evaluates the use of Parylene C and Parylene N as passivation layers for EG. Electronic transport of EG quantum Hall devices and non-contact microwave perturbation measurements of millimeter-sized areas of EG are both performed on bare and Parylene coated samples to test the efficacy of the passivation layers. The reported results, showing a significant improvement in passivation due to Parylene deposition, suggest a method for the mass production of millimeter-scale graphene devices with stable electrical properties., Competing Interests: Notes Commercial equipment, instruments, and materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology or the United States government, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose. The authors declare no competing financial interest.