Compressed Sensing in Scanning Tunneling Microscopy/Spectroscopy for Observation of Quasi-Particle Interference

Abstract

We applied a method of compressed sensing to the observation of quasi-particle interference (QPI) by scanning tunneling microscopy/spectroscopy to improve efficiency and save measurement time. To solve an ill-posed problem owing to the scarcity of data, the compressed sensing utilizes the sparseness of QPI patterns in momentum space. We examined the performance of a sparsity-inducing algorithm called least absolute shrinkage and selection operator (LASSO), and demonstrated that LASSO enables us to recover a double-circle QPI pattern of the Ag(111) surface from a dataset whose size is less than that necessary for the conventional Fourier transformation method. In addition, the smallest number of data required for the recovery is discussed on the basis of cross validation.The interference of electrons is one of the manifestations of their particle-wave duality in quantum mechanics. When electrons are scattered by local disordered structures, such as defects, adsorbates, and step edges on surfaces, the reflected electronic wave interferes with the injected one to form a spatial modulation in the local density of states (LDOS), that is, a quasiparticle interference (QPI) pattern. The modulated LDOS was first observed in real space by scanning tunneling microscopy and spectroscopy (STM/S) on noble metal surfaces. 1, 2) Analyzing a QPI pattern provides us with much information on the electronic states in momentum * equally contributed

Fast spectroscopic mapping of two-dimensional quantum materials

“…At this point, it is crucial to realize that STM investigations are amenable to compressive sensing concepts (20,21) because the data structure is oftentimes highly sparse or compressible in one representation space. In our example, this applies to the QPI pattern (17,22), which consists of only a few nonzero values in Fourier domain (Fig. 1b).…”

Sparse Modeling in Quantum Many-Body Problems

“…The MEM has typically been used for the inversion, 41,42) but compressed sensing is now an alternative. 43) Compressed sensing has also been applied to NMR spectroscopy for studying molecular dynamics, 44,45) scanning tunneling spectroscopy (STS)/scanning tunneling microscopy (STM) for investigating the k-space electronic properties from real-space measurements, 46) inverse X-ray fluorescence holography (IXFH) for deriving a three-dimensional image of atomic positions, 47) and X-ray absorption fine structure (XAFS) for elucidating atomic properties in solids. 48) The recent observation of a black hole shadow utilized the sparse-modeling technique because signals are received simultaneously at multiple observatories distributed worldwide and hence the sampling data are inevitably incomplete.…”

Compressed Sensing for STM imaging of defects and disorder

“…Most images in the natural world have a sparse frequency or wavelet representation, including those generated by scanning microscopies. Indeed, CS has been successfully implemented in scanning electron [13], atomic force [14], and piezoresponse force microscopy [15], and quasiparticle interference imaging by STS [3,16]. However, a detailed understanding of the potential of CS for STM has yet to be developed, particularly with respect to imaging defects and disorder.…”