使用部分递归星形-网状变换的基于石墨烯的量子霍尔阵列辅助计算
Auxiliary Calculations for Graphene-Based Quantum Hall Arrays Using Partially Recursive Star-Mesh Transformations
AI总结：
本文通过部分递归星形-网状变换方法，研究石墨烯基量子霍尔阵列器件中优化高有效量子化电阻所需元件数量的策略，发现至少一次完全递归可最大程度减少总元件数。
摘要：
先前用于优化石墨烯基量子霍尔阵列器件（QHARS）中获取高有效量子化电阻所需总器件元件数量的数学方法，已通过部分递归模式得到进一步探索。设计方案假定使用外延石墨烯元件，其在ν=2平台处的量子化霍尔电阻（R_H ≈ 12906.4 Ω）成为构建更大有效量子化电阻的基本单元。辅助计算表明，至少应用一次完全递归对于最大化减少高电阻所需的总QHARS元件数量具有重要意义。
英文摘要：
A previous mathematical approach adopted for optimizing the number of total device elements required for obtaining high effective quantized resistances in graphene-based quantum Hall array devices (QHARS) has been further explored with partial recursion patterns. Designs would assume the use of epitaxial graphene elements, whose quantized Hall resistance at the ν=2 plateau (R_H \approx 12906.4 \Ohm) becomes the building block for larger effective, quantized resistances. Auxiliary calculations suggest the importance of applying full recursions at least once to maximize the reduction of total QHARS elements needed for high resistances.
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