Bragg Interferometry of Moiré Superlattices: From Geometric Phase Principles to Atomic Reconstruction

Isaac M. Craig; D. Kwabena Bediako

Home/Archive/arXiv

arXiv · 2607.09901

Bragg Interferometry of Moiré Superlattices: From Geometric Phase Principles to Atomic Reconstruction

Isaac M. Craig·D. Kwabena Bediako

View original source ↗Read source document ↗Export metadata ↓

Abstract

The emergence of moiré superlattices formed by twisting and stacking two-dimensional materials has created a need for characterization techniques capable of mapping sub-angstrom atomic reconstruction across micron-scale fields of view. This review surveys a suite of methodologies developed to extract geometric phases in electron microscopy and X-ray spectroscopy, with a primary focus on the interference of overlapping Bragg reflections in the dark field. We provide a comparative analysis of some established techniques, including geometric phase analysis, converged beam electron diffraction holography, and various ptychographic paradigms, culminating in a discussion of Bragg interferometry for measuring interlayer displacement fields and strain in moiré materials. We demonstrate the utility of Bragg interferometry through case studies of twisted bilayer and trilayer graphene as well as transition metal dichalcogenide moiré systems. Special attention is given to the unique advantages of this dark-field interferometric method for probing buried interfaces and encapsulated heterostructures, as well as the inherent challenges of interpreting incomplete phase information in the presence of dynamical scattering. By examining the physical principles underlying these approaches, this review highlights the conceptual similarities and practical trade-offs involved in high-resolution structural mapping of materials in which the interplay between structural relaxation and electronic behavior defines a scientific frontier at the nexus of modern condensed matter physics, nanomaterials engineering, and interfacial chemistry.

Explore related subjects

cond-mat.mtrl-sci

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Isaac M. Craig, D. Kwabena Bediako. 2026-07-10. Bragg Interferometry of Moiré Superlattices: From Geometric Phase Principles to Atomic Reconstruction. https://arxiv.org/abs/2607.09901

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Towards ultra-scaled nanoelectronics using the zipper material system $Bi_2O_2Se/Bi_2SeO_5$

Two-dimensional (2D) materials could overcome the scaling bottleneck of nanoelectronics by enabling atomically thin channels, superior electrostatic control, and reduced short-channel effects. However, progress is limited by the lack of semiconductor–insulator interfaces being simultaneously scalable, stable, and reliable. Conventional 2D interfaces are often low quality or require transferring dissimilar materials, limiting reproducibility and scalability. We show that the zipper heterostructure formed by the high-mobility 2D semiconductor Bi 2 O 2 Se and its native high- κ oxide Bi 2 SeO 5 addresses these challenges, providing an atomically sharp, chemically matched interface with excellent electrostatics and promising scaling potential. We further present the first comprehensive multiscale assessment of Bi 2 O 2 Se/Bi 2 SeO 5 transistors targeting thermal stability, reliability, and scalability by linking atomic-scale structure and defects to device-level behavior across four transistor generations (top-gated, fin, and two gate-all-around architectures). Benchmarking against IRDS-2035 targets indicates that Bi 2 O 2 Se/Bi 2 SeO 5 devices could deliver high drive current with low gate leakage under aggressive scaling, potentially surpassing the targets in the upper-bound region of the sensitivity analysis. Finally, we identify oxygen-related oxide defects as the dominant origin of hysteresis consistent with a beneficial role of encapsulation and oxygen-rich annealing. Together, our findings support the potential of this zipper material system as a technologically-credible and manufacturing-relevant platform for future nanoelectronics.

cond-mat.mtrl-sci↗

arXiv2026

Influence of Heterogeneity on the Response of Architected Metamaterials

Architected metamaterials like foams and lattices exhibit complex responses governed by microstructural instabilities, localization, and phase-transition-like phenomena. Their behavior is further affected by heterogeneities inherent in their microstructure often caused through manufacturing processes. In this study we extend a gradient-enhanced, nonlocal continuum formulation to incorporate stochastic material heterogeneity through Gaussian random fields imposed on selected constitutive parameters. The framework enables independent control of both the amplitude and spatial correlation of material fluctuations while preserving thermodynamic consistency and regularization of localization. It also introduces a characteristic lengthscale ratio between the nonlocal and correlation lengthscales, that enables modeling at the limit of random or spatially correlated microstructures. Finite element simulations of confined compression and indentation show that heterogeneity fundamentally alters phase nucleation, localization morphology, and macroscopic response. Overall, the proposed framework provides a unified approach for linking stochastic material variability to instability-driven mechanics in architected metamaterials, enabling improved understanding of imperfection sensitivity, stability and design. It showcases how heterogeneity alone can influence characteristic features of the response, such as stability, slope of the plateau region, and elimination of the initial elastic regime.

cond-mat.mtrl-sci↗

arXiv2026

Structural, electronic, and optical properties of hexagonal GeSn from density functional theory

Unlike cubic GeSn, which undergoes an indirect-to-direct bandgap transition only above a finite Sn concentration, lonsdaleite (2H) germanium is an intrinsic direct-gap semiconductor. We employ first-principles density functional theory to investigate the structural, electronic, and optical properties of 2H-Ge$_{1-x}$Sn$_{x}$ random alloys in the dilute Sn regime ($x \le 0.10$). Substitutional disorder is modeled using 48-atom special quasirandom structure (SQS) supercells, and the coherent effective band structure is recovered via spectral band unfolding. We show that the semiconducting alloy configurations retain a direct bandgap at the $Γ$ point, with a moderate, nearly linear reduction of the bandgap in the dilute regime that shifts the fundamental absorption edge toward the mid-infrared. As the gap approaches zero, its calculated value becomes increasingly sensitive to the atomic configuration and supercell size. Evaluation of the optical transition matrix elements shows that the polarization anisotropy characteristic of pristine 2H-Ge remains observable under dilute Sn alloying. Although alloy disorder relaxes the crystal selection rules, the band edge response remains dominated by light polarized perpendicular to the crystal $c$ axis, whereas the parallel component remains weaker. These results identify dilute hexagonal GeSn as a tunable direct-gap system with a strongly polarization-dependent optical response in the infrared.

cond-mat.mtrl-sci↗