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arXiv · 2510.20575

Local Density of States as a Probe of Multifractality in Quasiperiodic Moir\'e Materials

Ricardo Oliveira·Nicolau Sobrosa·Pedro Ribeiro·Bruno Amorim·Eduardo V. Castro
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Abstract

Quasiperiodic moir\'e materials provide a new platform for realizing critical electronic states, yet a direct and experimentally practical method to characterize this criticality has been lacking. We show that a multifractal analysis of the local density of states (LDOS), accessible via scanning tunneling microscopy, offers an unambiguous signature of criticality from a single experimental sample. Applying this approach to a one-dimensional quasiperiodic model, a stringent test case due to its fractal energy spectrum, we find a clear distinction between the broad singularity spectra $f\left(\alpha\right)$ of critical states and the point-like spectra of extended states. We further demonstrate that these multifractal signatures remain robust over a wide range of energy broadenings relevant to experiments. Our results establish a model-independent, experimentally feasible framework for identifying and probing multifractality in the growing family of quasiperiodic and moir\'e materials.

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Ricardo Oliveira, Nicolau Sobrosa, Pedro Ribeiro, Bruno Amorim, Eduardo V. Castro. 2025-10-23. Local Density of States as a Probe of Multifractality in Quasiperiodic Moir\'e Materials. https://arxiv.org/abs/2510.20575

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