Dictionary learning in Fourier-transform scanning tunneling spectroscopy

Sky C. Cheung, John Y. Shin, Yenson Lau, Zhengyu Chen, Ju Sun, Yuqian Zhang, Marvin A. Müller, Ilya M. Eremin, John N. Wright () and Abhay N. Pasupathy ()
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Sky C. Cheung: Columbia University
John Y. Shin: Columbia University
Yenson Lau: Columbia University
Zhengyu Chen: Columbia University
Ju Sun: Columbia University
Yuqian Zhang: Columbia University
Marvin A. Müller: Ruhr-Universität Bochum
Ilya M. Eremin: Ruhr-Universität Bochum
John N. Wright: Columbia University
Abhay N. Pasupathy: Columbia University

Nature Communications, 2020, vol. 11, issue 1, 1-11

Abstract: Abstract Modern high-resolution microscopes 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 structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization 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 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.

Date: 2020
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DOI: 10.1038/s41467-020-14633-1

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