# Sparse Sampling for Fast Quasiparticle Interference Mapping

## TL;DR

This paper introduces a compressed sensing approach to significantly accelerate quasiparticle interference mapping in STM, enabling faster data collection while maintaining high-quality results, thus opening new avenues for studying quantum materials.

## Contribution

The paper demonstrates the use of compressed sensing to speed up QPI mapping in STM, reducing measurement time without sacrificing data quality.

## Key findings

- Reliable recovery of QPI information from fewer measurements
- Effective random sampling strategies for QPI data acquisition
- Enhanced efficiency through optimized STM tip movement

## Abstract

Scanning tunneling microscopy (STM) is a notoriously slow technique; Data-recording is serial which renders complex measurement tasks, such as quasiparticle interference (QPI) mapping, impractical. However, QPI would provide insight into band-structure details of quantum materials which can be inaccessible to angle-resolved photoemission spectroscopy. Here we use compressed sensing (CS) to fundamentally speed-up QPI mapping. We reliably recover the QPI information from a fraction of the usual local density of state measurements. The requirement of CS is naturally fulfilled for QPI, since CS relies on sparsity in a vector domain, here given by few nonzero coefficients in Fourier space. We exemplify CS on a simulated Cu(111) surface using random sampling of constant and varying probability density. We further simplify the motion of the STM tip through an open traveling salesman's problem for greater efficiency. We expect that the implications of our CS approach will be transformative for the exploration of 2D quantum materials.

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Source: https://tomesphere.com/paper/1908.01903