Visualization of multifractal superconductivity in a two-dimensional transition metal dichalcogenide in the weak-disorder regime

TL;DR

This study visualizes multifractal superconductivity in a two-dimensional weakly disordered NbSe₂, revealing spatial inhomogeneity and anomalous scaling consistent with theoretical models of 2D disordered systems.

Contribution

It provides experimental evidence of multifractal features in 2D superconductors under weak disorder using scanning tunneling microscopy/spectroscopy.

Findings

Superconducting gap exhibits spatial modulation aligned with quasiparticle interference patterns.

Gap width distribution follows a log-normal pattern and shows power-law decay in correlations.

Experimental singularity spectrum displays anomalous scaling typical of 2D weakly disordered systems.

Abstract

Eigenstate multifractality is a distinctive feature of non-interacting disordered metals close to a metal-insulator transition, whose properties are expected to extend to superconductivity. While multifractality in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, multifractality in 2D systems is expected to be observable even for weak disorder. Here we provide evidence for multifractal features in the superconducting state of an intrinsic weakly disordered single-layer NbSe$_2$ by means of low-temperature scanning tunneling microscopy/spectroscopy. The superconducting gap, characterized by its width, depth and coherence peaks' amplitude, shows a characteristic spatial modulation coincident with the periodicity of the quasiparticle interference pattern. Spatial inhomogeneity of the superconducting gap width, proportional to the local order parameter in the weak-disorder regime, follows a log-normal statistical distribution as well as a power-law decay of the two-point correlation function, in agreement with our theoretical model. Furthermore, the experimental singularity spectrum f($\alpha$) shows anomalous scaling behavior typical from 2D weakly disordered systems.