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

TL;DR

This paper proposes using multifractal analysis of the local density of states, accessible via scanning tunneling microscopy, as a practical method to identify critical states in quasiperiodic moiré materials, validated on a 1D model.

Contribution

It introduces a model-independent, experimentally feasible approach to detect multifractality in quasiperiodic materials through LDOS analysis.

Findings

Distinct multifractal spectra for critical vs. extended states

Method remains robust over relevant experimental energy broadenings

Applicable to various quasiperiodic and moiré materials

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.