Dictionary learning in Fourier-transform scanning tunneling spectroscopy.

Modern high-resolution microscopes are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material.

Volume-wise destruction of the antiferromagnetic Mott insulating state through quantum tuning.

RENiO3 (RE=rare-earth element) and V2O3 are archetypal Mott insulator systems. When tuned by chemical substitution (RENiO3) or pressure (V2O3), they exhibit a quantum phase transition (QPT) between an antiferromagnetic Mott insulating state and a paramagnetic metallic state. Because novel physics often appears near a Mott QPT, the details of this transition, such as whether it is first or second order, are important. Here, we demonstrate through muon spin relaxation/rotation (µSR) experiments that the QPT in RENiO3 and V2O3 is first order: the magnetically ordered volume fraction decreases to zero at the QPT, resulting in a broad region of intrinsic phase separation, while the ordered magnetic moment retains its full value until it is suddenly destroyed at the QPT. These findings bring to light a surprising universality of the pressure-driven Mott transition, revealing the importance of phase separation and calling for further investigation into the nature of quantum fluctuations underlying the transition.

Ferromagnetic ordering in superatomic solids.

In order to realize significant benefits from the assembly of solid-state materials from molecular cluster superatomic building blocks, several criteria must be met. Reproducible syntheses must reliably produce macroscopic amounts of pure material; the cluster-assembled solids must show properties that are more than simply averages of those of the constituent subunits; and rational changes to the chemical structures of the subunits must result in predictable changes in the collective properties of the solid. In this report we show that we can meet these requirements. Using a combination of magnetometry and muon spin relaxation measurements, we demonstrate that crystallographically defined superatomic solids assembled from molecular nickel telluride clusters and fullerenes undergo a ferromagnetic phase transition at low temperatures. Moreover, we show that when we modify the constituent superatoms, the cooperative magnetic properties change in predictable ways.