Non-uniform Recovery Guarantees for Binary Measurements and Infinite-Dimensional Compressed Sensing

Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclear Magnetic Resonance (NMR), radio interferometry, helium atom scattering etc., the theory of compressed sensing with Fourier transform measurements has reached a mature level. However, for binary measurements via the Walsh transform, the theory has long been merely non-existent, despite the large number of applications such as fluorescence microscopy, single pixel cameras, lensless cameras, compressive holography, laser-based failure-analysis etc. Binary measurements are a mainstay in signal and image processing and can be modelled by the Walsh transform and Walsh series that are binary cousins of the respective Fourier counterparts. We help bridging the theoretical gap by providing non-uniform recovery guarantees for infinite-dimensional compressed sensing with Walsh samples and wavelet reconstruction. The theoretical results demonstrate that compressed sensing with Walsh samples, as long as the sampling strategy is highly structured and follows the structured sparsity of the signal, is as effective as in the Fourier case. However, there is a fundamental difference in the asymptotic results when the smoothness and vanishing moments of the wavelet increase. In the Fourier case, this changes the optimal sampling patterns, whereas this is not the case in the Walsh setting.

Electron–phonon coupling in superconducting 1T-PdTe2

We have determined the electron–phonon interaction in type II Dirac semimetallic 1T-PdTe2 by means of helium atom scattering. While 1T-PdTe2 is isostructural with 1T-PtTe2, only the former is superconductor. The difference can be traced to the substantially larger value of the electron–phonon coupling in 1T-PdTe2, λ = 0.58, obtained from the Debye-Waller attenuation of the He specular peak. With this value and the surface Debye temperature, ΘD = 106.2 K, we have figured out the superconducting critical temperature, Tc = 1.83 K given by the BCS theory, which is in good agreement with Tc = (1.95 ± 0.03) K obtained with low-temperature scanning tunneling microscopy. The value of the effective mass related to ΘD indicates that the large electron–phonon coupling in 1T-PdTe2 is due to coupling, not only with the zone-center optical mode O2 at 9.2 meV, as proposed in a recent theoretical study, but also with the zone-boundary acoustic mode LA. Our results suggest that the topological states of a Dirac cone play a negligible role on the onset of superconductivity.

Inter-adsorbate forces and coherent scattering in helium spin-echo experiments

Using helium atom scattering to identify adsorbate interactions and separate the effects of long and short range forces.

Helium atom scattering from potassium tantalate/niobate(001) surfaces

The specular diffraction intensity of helium atoms from KTa0.48Nb0.52O3 surfaces undergoes dramatic fluctuations as a function of surface temperature.

Inelastic helium atom scattering from Sb2Te3(111): phonon dispersion, focusing effects and surfing

We report the surface phonon dispersion of the topological insulator Sb2Te3 together with a number of additional inelastic events, including resonance enhancement, kinematical focusing and surfing.

Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering

Helium-atom scattering (HAS) spectroscopy from conducting surfaces has been shown to provide direct information on the electron–phonon interaction, more specifically the mass-enhancement factor λ from the temperature dependence of the Debye–Waller exponent, and the mode-selected electron–phonon coupling constants λQν from the inelastic HAS intensities from individual surface phonons. The recent applications of the method to superconducting ultra-thin films, quasi-1D high-index surfaces, and layered transition-metal and topological pnictogen chalcogenides are briefly reviewed.

Prominent out-of-plane diffraction in helium scattering from a methyl-terminated Si(111) surface

Out-of-plane diffraction widely surpasses in-plane diffraction in helium atom scattering from methyl-terminated Si(111) surfaces.