Fractal-like star-mesh transformations using graphene quantum Hall arrays

• Main Authors: Scaletta, Dominick S, Mhatre, Swapnil M, Tran, Ngoc Thanh Mai, Yang, Cheng-Hsueh, Hill, Heather M, Yang, Yanfei, Meng, Linli, Panna, Alireza R, Payagala, Shamith U, Elmquist, Randolph E, Jarrett, Dean G, Newell, David B, Rigosi, Albert F
• Format: Journal Article
• Language: English
• Published: 27.09.2023
• Subjects: Physics - Applied Physics; Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.2309.15813

A mathematical approach is adopted for optimizing the number of total device elements required for obtaining high effective quantized resistances in graphene-based quantum Hall array devices. This work explores an analytical extension to the use of star-mesh transformations such that fractal-like, or recursive, device designs can yield high enough resistances (like 1 E{\Omega}, arguably the highest resistance with meaningful applicability) while still being feasible to build with modern fabrication techniques. Epitaxial graphene elements are tested, whose quantized Hall resistance at the nu=2 plateau (R_H = 12906.4 {\Omega}) becomes the building block for larger effective, quantized resistances. It is demonstrated that, mathematically, one would not need more than 200 elements to achieve the highest pertinent resistances