Sparse Sampling and Nonlinear Spectroscopy for Fast Quasiparticle Interference Imaging

Quasiparticle Interference (QPI) Imaging with the scanning tunneling microscope (STM) is becoming an important tool in the investigation of advanced quantum materials. It provides insight into the band-structure for experimental conditions that do not permit the use of angular resolved photoemission spectroscopy, such as in high magnetic fields, at ultra-low temperatures, or on small field-effect devices. However, QPI imaging is also very slow because it requires the measurements of a massive amount of energy dependent local density of states (LDOS) that can occupy an STM for weeks. We demonstrate orders of magnitude faster imaging by our combination of sparse sampling and parallel spectroscopy. Sparse sampling reduces the number of required LDOS measurements and parallel spectroscopy accelerates the individual point spectrum. These two methods provide substantial speed enhancements individually but make QPI imaging vastly faster when used in combination because of their multiplicative dependence. As an introduction we measure the QPI of Au(111) and Bi2212 at a thousandfold faster mapping and show the straightforward implementation into existing SPM systems without the need for recabling of one's apparatus.