Dictionary Learning in Fourier Transform Scanning Tunneling Spectroscopy

TL;DR

This paper introduces a novel nonconvex optimization algorithm for analyzing microscopy images, outperforming Fourier analysis in extracting fundamental motifs and phase information, demonstrated on superconducting material images.

Contribution

The paper presents a new algorithm that directly uncovers motifs in real-space images, providing phase-sensitive information and superior analysis over traditional Fourier methods.

Findings

Successfully recovered quasiparticle interference in a superconductor

Provided phase-sensitive insights into pairing symmetry in NaFeAs

Demonstrated quantitative superiority over Fourier analysis

Abstract

Modern high-resolution microscopes, such as the scanning tunneling microscope, are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the underlying structure of fundamental motifs present in an image. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of a new algorithm based on nonconvex optimization, applicable to any microscopy modality, that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this novel algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material. Our phase sensitive quasiparticle interference imaging results indicate that the pairing symmetry in optimally doped NaFeAs is consistent with a sign-changing s+- order parameter.