Sparse sampling for fast quasiparticle-interference mapping

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 could provide insight into band-structure details of quantum materials that 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 uniform and varying probability density. The latter improves QPI recovery and mitigates Fourier artifacts. We further simplify the motion of the STM tip through an open traveling salesman's problem for greater efficiency and use the tip-path for drift correction. We expect that the implications of our CS approach will be transformative for the exploration of two-dimensional quantum materials

Fast spectroscopic mapping of two-dimensional quantum materials

The discovery of quantum materials entails extensive spectroscopic studies that are carried out against multitudes of degrees of freedom, such as magnetic field, location, temperature, or doping. As this traditionally involves two or more serial measurement tasks, spectroscopic mapping can become excruciatingly slow. We demonstrate orders of magnitude faster measurements through our combination of sparse sampling and parallel spectroscopy. We exemplify our concept using quasiparticle interference imaging of Au(111) and Bi2Sr2CaCu2O8+δ (Bi2212), as two well-known model systems. Our method is accessible, straightforward to implement with existing setups, and can be easily extended to promote gate or field spectroscopy. In view of further substantial speed advantages, it is setting the stage to fundamentally promote the discovery of quantum materials

Adaptive sparse sampling for quasiparticle interference imaging

Quasiparticle interference imaging (QPI) offers insight into the band structure of quantum materials from the Fourier transform of local density of states (LDOS) maps. Their acquisition with a scanning tunneling microscope is traditionally tedious due to the large number of required measurements that may take several days to complete. The recent demonstration of sparse sampling for QPI imaging showed how the effective measurement time could be fundamentally reduced by only sampling a small and random subset of the total LDOS. However, the amount of required sub-sampling to faithfully recover the QPI image remained a recurring question. Here we introduce an adaptive sparse sampling (ASS) approach in which we gradually accumulate sparsely sampled LDOS measurements until a desired quality level is achieved via compressive sensing recovery. The iteratively measured random subset of the LDOS can be interleaved with regular topographic images that are used for image registry and drift correction. These reference topographies also allow to resume interrupted measurements to further improve the QPI quality. Our ASS approach is a convenient extension to quasiparticle interference imaging that should remove further hesitation in the implementation of sparse sampling mapping schemes

Adaptive Sparse Sampling for Quasiparticle Interference Imaging

Quasiparticle interference imaging (QPI) offers insight into the band structure of quantum materials from the Fourier transform of local density of states (LDOS) maps. Their acquisition with a scanning tunneling microscope is traditionally tedious due to the large number of required measurements that may take several days to complete. The recent demonstration of sparse sampling for QPI imaging showed how the effective measurement time could be fundamentally reduced by only sampling a small and random subset of the total LDOS. However, the amount of required sub-sampling to faithfully recover the QPI image remained a recurring question. Here we introduce an adaptive sparse sampling (ASS) approach in which we gradually accumulate sparsely sampled LDOS measurements until a desired quality level is achieved via compressive sensing recovery. The iteratively measured random subset of the LDOS can be interleaved with regular topographic images that are used for image registry and drift correction. These reference topographies also allow to resume interrupted measurements to further improve the QPI quality. Our ASS approach is a convenient extension to quasiparticle interference imaging that should remove further hesitation in the implementation of sparse sampling mapping schemes.Comment: 10 pages, 5 figure

Weak-signal extraction enabled by deep-neural-network denoising of diffraction data

Removal or cancellation of noise has wide-spread applications for imaging and acoustics. In every-day-life applications, denoising may even include generative aspects which are unfaithful to the ground truth. For scientific applications, however, denoising must reproduce the ground truth accurately. Here, we show how data can be denoised via a deep convolutional neural network such that weak signals appear with quantitative accuracy. In particular, we study X-ray diffraction on crystalline materials. We demonstrate that weak signals stemming from charge ordering, insignificant in the noisy data, become visible and accurate in the denoised data. This success is enabled by supervised training of a deep neural network with pairs of measured low- and high-noise data. This way, the neural network learns about the statistical properties of the noise. We demonstrate that using artificial noise (such as Poisson and Gaussian) does not yield such quantitatively accurate results. Our approach thus illustrates a practical strategy for noise filtering that can be applied to challenging acquisition problems.Comment: 8 pages, 4 figure

A sacrificial magnet concept for field dependent surface science studies

ABSTRACT: We demonstrate a straightforward approach to integrating a magnetic field into a low-temperature scanning tunneling microscope (STM) by adhering an NdFeB permanent magnet to a magnetizable sample plate. To render our magnet concept compatible with high-temperature sample cleaning procedures, we make the irreversible demagnetization of the magnet a central part of our preparation cycle. After sacrificing the magnet by heating it above its Curie temperature, we use a transfer tool to attach a new magnet in-situ prior to transferring the sample into the STM. We characterize the magnetic field created by the magnet using the Abrikosov vortex lattice of superconducting NbSe2. Excellent agreement between the distance dependent magnetic fields from experiments and simulations allows us to predict the magnitude and orientation of magnetic flux at any location with respect to the magnet and the sample plate. Our concept is an accessible solution for field-dependent surface science studies that require fields in the range of up to 400 mT and otherwise detrimental heating procedures. • Accessible magnetic field generation. • Selectable field strength and orientation. • Compatible with high-temperature sample preparation

Weak signal extraction enabled by deep neural network denoising of diffraction data

The removal or cancellation of noise has wide-spread applications in imaging and acoustics. In applications in everyday life, such as image restoration, denoising may even include generative aspects, which are unfaithful to the ground truth. For scientific use, however, denoising must reproduce the ground truth accurately. Denoising scientific data is further challenged by unknown noise profiles. In fact, such data will often include noise from multiple distinct sources, which substantially reduces the applicability of simulation-based approaches. Here we show how scientific data can be denoised by using a deep convolutional neural network such that weak signals appear with quantitative accuracy. In particular, we study X-ray diffraction and resonant X-ray scattering data recorded on crystalline materials. We demonstrate that weak signals stemming from charge ordering, insignificant in the noisy data, become visible and accurate in the denoised data. This success is enabled by supervised training of a deep neural network with pairs of measured low- and high-noise data. We additionally show that using artificial noise does not yield such quantitatively accurate results. Our approach thus illustrates a practical strategy for noise filtering that can be applied to challenging acquisition problems