14.12.2020, 10:00 CET

Fabian Natterer
University of Zurich, Switzerland

“All that glitters is gold”: First Impressions of Sparse Sampling for fast Quasiparticle Interference measurements with Au(111) Surface State

The band structure conveys the most fundamental information of a material that enables a prediction of important properties, such as its transport behavior, the presence of superconducting phases, optical transitions, magnetism etc. However, theoretical modelling of novel quantum materials, often require an experimental verification in conditions in which established methods, such as ARPES are inhibited by the involvement of magnetic fields, milli Kelvin temperatures, or device geometries. Although the complementary method, scanning tunneling microscopy (STM) based quasiparticle interference (QPI) mapping (1), operates well in such conditions, its band-structure mapping via the scattering space is also excruciatingly slow. Here we investigate the promise of a compressed sensing implementation of QPI measurements with STM that fundamentally speeds up large scale spectroscopic mapping of the local density of states (LDOS)(2). The condition for compressive sensing is fulfilled by the sparsity of the LDOS information in the reciprocal domain, which is also the sought QPI pattern. We utilize the Shockley surface state of Au(111) as a well-studied model system for our QPI implementation(3, 4). Instead of visiting all points on a regular grid, we only visit a random and small fraction of the usual measurement locations for which we use a traveling salesperson optimization to reduce tip-motion related overhead. This random walk separates time and spatial correlation that previously got intermixed in conventional grid mapping schemes and that were particularly problematic for periodic perturbations, such as line-noise or mechanical resonances. Our sparse QPI implementation substantially reduces the overall measurement time without the introducing of artifacts. Looking at the QPI maps of Au(111), we not only find the expected near-free electron dispersion reported before but also a band-gap that can be traced back to the action of the period potential of the herringbone reconstruction (5, 6). We finally discuss limitations and opportunities of the sparse QPI method.1.  L. Petersen, Ph. Hofmann, E. W. Plummer, F. Besenbacher, Fourier Transform–STM: determining the surface Fermi contour. J. Electron Spectrosc. Relat. Phenom. 109, 97–115 (2000).2.  J. Oppliger, F. D. Natterer, Sparse sampling for fast quasiparticle-interference mapping. Phys. Rev. Res. 2, 023117 (2020).3.  S. LaShell, B. A. McDougall, E. Jensen, Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy. Phys. Rev. Lett. 77, 3419–3422 (1996).4.  F. Reinert, G. Nicolay, S. Schmidt, D. Ehm, S. Hüfner, Direct measurements of the L-gap surface states on the (111) face of noble metals by photoelectron spectroscopy. Phys. Rev. B. 63, 115415 (2001).5.  W. Chen, V. Madhavan, T. Jamneala, M. F. Crommie, Scanning Tunneling Microscopy Observation of an Electronic Superlattice at the Surface of Clean Gold. Phys. Rev. Lett. 80, 1469–1472 (1998).6.  F. Reinert, G. Nicolay, Influence of the herringbone reconstruction on the surface electronic structure of Au(111). Appl. Phys. A. 78, 817–821 (2004).