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arXiv · 2502.19017

Emergent fractals in hBN-encapsulated graphene based supermoir\'e structures and their experimental signatures

Deepanshu Aggarwal·Rohit Narula·Sankalpa Ghosh
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Abstract

Supermoir\'e structures (SMS), formed by overlapping moir\'e-patterns in van der Waals heterostructures, display complex behaviour that lacks a comprehensive low-energy theoretical description. We demonstrate that these structures can form emergent fractals under specific conditions and identify the parameter space where this occurs in hexagonal trilateral SMS. This fractality enables a reliable calculation of low-energy band counts, which are crucial for understanding both single-particle and correlation effects. Using an effective Hamiltonian that includes in- and out-of-plane lattice relaxation, we analyze SMS in hBN-encapsulated single and bilayer graphene. We prescribe methods to experimentally verify these fractals and extract their fractal dimension through angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM).

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Deepanshu Aggarwal, Rohit Narula, Sankalpa Ghosh. 2025-02-26. Emergent fractals in hBN-encapsulated graphene based supermoir\'e structures and their experimental signatures. https://arxiv.org/abs/2502.19017

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