A traveling salesperson and sparse sampling boost to quasiparticle interference mapping*

The serial nature of STM investigations render complex measurement tasks, such as QPI mapping, impractical. Conventionally, QPI is carried out by recording hundreds of thousands of point-spectra that capture LDOS modulations from which scattering-space is calculated via Fourier-transform. Yet, despite the efforts required, QPI is mapped extensively because it provides insight into band-structure details when measurement conditions prohibit the use of ARPES. However, in view of the large number of data-points, it is surprising that QPI patterns contain only little information. This motivates our use of compressed sensing (CS) to fundamentally speed-up QPI mapping [1]. From only a fraction of the usual LDOS measurements, we reliably recover the full QPI pattern. Since CS depends on incoherent measurements, we sparsely sample LDOS at randomly selected locations using constant and varying probability density. The STM tip is moved between LDOS measurements according to a traveling salesperson to achieve an overall 5-50 faster QPI throughput.
[1] J. Oppliger and F.D. Natterer, arXiv 1908.01903