Algorithms for determining resistances in quantum Hall annuli with p-n junctions

TL;DR

This paper investigates quantized resistance behaviors in graphene Corbino p-n junction devices, combining experimental observations with numerical simulations to support scalable fabrication methods for advanced electronic applications.

Contribution

It introduces empirical formulae for resistance in multi-terminal graphene p-n junctions, validated by experiments and simulations, aiding device scalability.

Findings

Unusual quantized resistances observed at the i=2 plateau

Empirical formulae accurately model experimental and simulated data

Ultraviolet lithography enables scalable device fabrication

Abstract

Just a few of the promising applications of graphene Corbino pnJ devices include two-dimensional Dirac fermion microscopes, custom programmable quantized resistors, and mesoscopic valley filters. In some cases, device scalability is crucial, as seen in fields like resistance metrology, where graphene devices are required to accommodate currents of the order 100 {\mu}A to be compatible with existing infrastructure. However, fabrication of these devices still poses many difficulties. In this work, unusual quantized resistances are observed in epitaxial graphene Corbino p-n junction devices held at the i=2 plateau and agree with numerical simulations performed with the LTspice circuit simulator. The formulae describing experimental and simulated data are empirically derived for generalized placement of up to three current terminals and accurately reflects observed partial edge channel cancellation. These results support the use of ultraviolet lithography as a way to scale up graphene-based devices with suitably narrow junctions that could be applied in a variety of subfields