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The discovery and analysis of X-ray diffraction from crystals by Max von Laue, William Henry Bragg and William Lawrence Bragg in 1912 marked the birth of crystallography. Over the last century, crystallography has been fundamental to the development of many fields of science. However, many samples in physics, chemistry, materials science, nanoscience, geology, and biology are non-crystalline, and thus their 3D structures are not accessible by traditional crystallography. Overcoming this hurdle has required the development of new structure determination methods. In this talk, I will present two methods that can go beyond crystallography: coherent diffractive imaging (CDI) and atomic electron tomography (AET). In CDI, the diffraction pattern of a non-crystalline sample or a nanocrystal is first measured and then directly phased to obtain an image. The well-known phase problem is solved by combining the oversampling method with iterative algorithms. In the first part of the talk, I will briefly discuss the principle of CDI and highlight its capability of direct observation of 3D topological spin textures and their interactions in a ferromagnetic superlattice. In the second part of the talk, I will present a general tomographic method, termed AET, for 3D structure determination of crystal defects and disordered materials at the single atomic level. By combining advanced electron microscopes with powerful computational algorithms, AET has been used to reveal the 3D atomic structure of crystal defects and chemical order/disorder and to precisely localize the 3D coordinates of individual atoms in materials without assuming crystallinity. The experimentally measured coordinates can then be used as direct input for quantum mechanical calculations of material properties such as atomic spin and orbital magnetic moments and local magnetocrystalline anisotropy. As coherent X-ray sources and powerful electron microscopes are under rapid development around the world, we expect that CDI and AET will find broad applications in both the physical and biological sciences.

Atomically thin or two-dimensional (2D) materials can be assembled into bespoke heterostructures to produce some extraordinary physical phenomena. Likewise, these highly tunable materials are useful platforms for exploring fundamental questions of interfacial chemical/electrochemical reactivity. One exciting and relatively recent example is the formation of moiré superlattices from azimuthally misoriented (twisted) layers. These moiré superlattices result in flat bands that lead to an array of correlated electronic phases. However, in these systems, complex strain relaxation can also strongly influence the fragile electronic states of the material. Precise characterization of these materials and their properties is therefore critical to the understanding of the behavior of these novel moiré materials (and 2D heterostructures in general). In this talk, I will discuss how spontaneous mechanical deformations (atomic reconstruction) and resultant intralayer strain fields at moiré superlattices of twisted bilayer graphene have been quantitatively imaged using 4D-STEM Bragg interferometry. I will also discuss the impact of these mechanical deformations to the electronic band structure of these moiré superlattices and the correlated electronic phases they host. The talk will then explore how various degrees of freedom that are unique to 2D materials may be used to tailor interfacial chemistry at well-defined mesoscopic electrodes and the outlook for new paradigms of functional materials for energy conversion and low-power electronic devices.

Uncovering structure/function relationships in condensed phase electronic materials is increasingly important for applications from solar energy to quantum optoelectronics. In this talk, we will explore multimodal microscopy to the role of microscopic heterogeneity and defects in emerging semiconductors, focusing on halide perovskites as a system that is not only technologically important, but also scientifically challenging. Halide perovskites are soft, and easily damaged by low doses of electrons. They are also complicated mixed conductors, exhibiting electronic and ionic relaxation dynamics that vary across many orders of magnitude in time and space. To probe these systems, we combine hyperspectral optical spectroscopy, electron microscopy, scanning probe microscopy, and data science tools to understand and control defects for applications in photovoltaics, showing how surface and grain boundary passivation enables the growth of films that approach thermodynamic efficiency limits for performance, while also problem the role of processing additives on microstructure and performance.

Properties and functions of molecular materials often emerge from intermolecular interactions and associated nanoscale structure and morphology. However, defects and disorder disturb the performance of, e.g., molecular electronic or photonic materials. We address these outstanding problems in several novel combinations of spatio-spectral and spatio-temporal infrared nano-imaging. In this talk I will give an overview of these new developments with a focus on intermolecular coupling induced molecular wavefunction delocalization and its disturbance through structural disorder. This provides for a molecular ruler to imagine structure, coupling, and dynamics of elementary processes on their elementary nanometer-femtosecond scales. I will further demonstrate how Purcell-enhanced and strongly coupled vibrational light matter interactions provide for new modalities in molecular nano-metrology and -sensing. I will conclude with a perspective how these novel quantum-enhanced modalities provide for qualitatively novel functional imaging as new tools to guide molecular device fabrication with improved performance.

Conventional optical microscopy focuses on designing optical systems to faithly replicate an image of a magnified object to reveal very small spatial features. Image quality, and thus the ability to observe small spatial features, is limited by the ability to form high quality images for widefield microscopy, or for focusing to the smallest possible spot for laser scanning microscopy. Computational imaging can sidestep such limitations by taking into account a model of the image process, and this way computational imaging is able to produce high resolution imaging with a greater flexibility for optical systems. I will provide an overview of several recent results on computational imaging from my group: 1) three dimensional widefield second harmonic generation tomographic imaging based in defocused illumination, 2) tomographic fluorescent imaging by mimicking coherent light propagation, and 3) saturated super deconvolution microscopy.