Fabrication of graphene-based quantum Hall networks and influences of partial star-mesh recursion

Materials Research Express Inclusive Publishing Trusted Science logo. Purpose-Led Publishing logo. Paper • The following article is Open access Fabrication of graphene-based quantum Hall networks and influences of partial star-mesh recursion Dominick S Scaletta, Ngoc Thanh Mai Tran, Marta Musso, Valery Ortiz Jimenez, Heather M Hill, Dean G Jarrett, Massimo Ortolano, Curt A Richter, David B Newell and Albert F Rigosi* Published 1 June 2026 • © 2026 The Author(s). Published by IOP Publishing Ltd Materials Research Express, Volume 13, Number 11 Focus Collection on Fundamental Aspects and Innovations in Quantum Materials Citation Dominick S Scaletta et al 2026 Mater. Res. Express 13 115601DOI 10.1088/2053-1591/ae7250 Download Article PDF Download PDF Article metrics 154 Total downloads Submit Submit to this Journal Share this article Abstract This work presents a substantial advancement on how one may develop high-resistance quantized Hall array resistance standards (QHARS) by using star-mesh transformations for element count minimization. More specifically, this work introduces a generalized mathematical reconciliation to recover exact effective quantized resistances found by simulation and measurement. Furthermore, this work explores the concept of fractal dimension, clarifying the benefits of both full and partial recursions in QHARS devices. Three different partial recursion cases are visited for a near-1 GΩ QHARS device. These partial recursions, analyzed in the context of their fractal dimensions, offer increased flexibility in accessing desired resistances within a specific neighborhood of values compared to full recursion methods, though at the cost of the number of required elements.