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

TL;DR

This paper presents an algorithm to predict fractional quantized resistances in graphene p-n junctions with multiple terminals, supported by experimental data, and applicable to other quantum Hall systems.

Contribution

It introduces a novel theoretical algorithm for calculating fractional quantized resistances in multi-terminal graphene p-n junctions, independent of material specifics.

Findings

Fractional resistance values are predicted as fractions of the quantum Hall resistance.

Experimental data from graphene devices confirm the theoretical predictions.

The formulation is applicable to other materials exhibiting quantum Hall effects.

Abstract

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 $R_H \approx 12906 {\Omega}$ 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.