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

Dominick S. Scaletta; Swapnil M. Mhatre; Ngoc Thanh Mai Tran; Cheng-Hsueh Yang; Heather M. Hill; Yanfei Yang; Linli Meng; Alireza R. Panna; Shamith U. Payagala; Randolph E. Elmquist; Dean G. Jarrett; David B. Newell; Albert F. Rigosi

arXiv · 2309.15813

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

Dominick S. Scaletta·Swapnil M. Mhatre·Ngoc Thanh Mai Tran·Cheng-Hsueh Yang·Heather M. Hill·Yanfei Yang·Linli Meng·Alireza R. Panna·Shamith U. Payagala·Randolph E. Elmquist·Dean G. Jarrett·David B. Newell·Albert F. Rigosi

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Abstract

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

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Dominick S. Scaletta, Swapnil M. Mhatre, Ngoc Thanh Mai Tran, Cheng-Hsueh Yang, Heather M. Hill, Yanfei Yang, Linli Meng, Alireza R. Panna, Shamith U. Payagala, Randolph E. Elmquist, Dean G. Jarrett, David B. Newell, Albert F. Rigosi. 2023-09-27. Fractal-like star-mesh transformations using graphene quantum Hall arrays. https://arxiv.org/abs/2309.15813

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