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Billions of organic molecules are known, but only a tiny fraction of the functional inorganic materials have been discovered, a particularly relevant problem to the community searching for new quantum materials. Recent advancements in machine-learning-based generative models, particularly diffusion models, show great promise for generating new, stable materials. However, integrating geometric patterns into materials generation remains a challenge. Here, we introduce Structural Constraint Integration in the GENerative model (SCIGEN). Our approach can modify any trained generative diffusion model by strategic masking of the denoised structure with a diffused constrained structure prior to each diffusion step to steer the generation toward constrained outputs. Furthermore, we mathematically prove that SCIGEN effectively performs conditional sampling from the original distribution, which is crucial for generating stable constrained materials. We generate eight million compounds using Archimedean lattices as prototype constraints, with over 10% surviving a multi-staged stability pre-screening. High-throughput density functional theory (DFT) on 26,000 survived compounds shows that over 50% passed structural optimization at the DFT level. Since the properties of quantum materials are closely related to geometric patterns, our results indicate that SCIGEN provides a general framework for generating quantum materials candidates., Comment: 512 pages total, 4 main figures + 218 supplementary figures

Optical properties in solids, such as refractive index and absorption, hold vast applications ranging from solar panels to sensors, photodetectors, and transparent displays. However, first-principles computation of optical properties from crystal structures is a complex task due to the high convergence criteria and computational cost. Recent progress in machine learning shows promise in predicting material properties, yet predicting optical properties from crystal structures remains challenging due to the lack of efficient atomic embeddings. Here, we introduce GNNOpt, an equivariance graph-neural-network architecture featuring automatic embedding optimization. This enables high-quality optical predictions with a dataset of only 944 materials. GNNOpt predicts all optical properties based on the Kramers-Kr{\"o}nig relations, including absorption coefficient, complex dielectric function, complex refractive index, and reflectance. We apply the trained model to screen photovoltaic materials based on spectroscopic limited maximum efficiency and search for quantum materials based on quantum weight. First-principles calculations validate the efficacy of the GNNOpt model, demonstrating excellent agreement in predicting the optical spectra of unseen materials. The discovery of new quantum materials with high predicted quantum weight, such as SiOs which hosts exotic quasiparticles, demonstrates GNNOpt's potential in predicting optical properties across a broad range of materials and applications., Comment: (i) Completely Rewritten Manuscript, including 5 main figures and 1 table. (ii) Supplementary Information, including 15 supplementary figures and 2 tables

Majorana zero modes (MZMs), emerging as exotic quasiparticles that carry non-Abelian statistics, hold great promise for achieving fault-tolerant topological quantum computation. A key signature of the presence of MZMs is the zero-bias peaks (ZBPs) from tunneling differential conductance. However, the identification of MZMs from ZBPs has faced tremendous challenges, due to the presence of topological trivial states that generate spurious ZBP signals. In this work, we introduce a machine-learning framework that can discern MZM from other signals using ZBP data. Quantum transport simulation from tight-binding models is used to generate the training data, while persistent cohomology analysis confirms the feasibility of classification via machine learning. In particular, even with added data noise, XGBoost classifier reaches $85\%$ accuracy for 1D tunneling conductance data and $94\%$ for 2D data incorporating Zeeman splitting. Tests on prior ZBP experiments show that some data are more likely to originate from MZM than others. Our model offers a quantitative approach to assess MZMs using ZBP data. Furthermore, our results shed light on the use of machine learning on exotic quantum systems with experimental-computational integration.

The precise controllability of the Fermi level is a critical aspect of quantum materials. For topological Weyl semimetals, there is a pressing need to fine-tune the Fermi level to the Weyl nodes and unlock exotic electronic and optoelectronic effects associated with the divergent Berry curvature. However, in contrast to 2D materials, where the Fermi level can be controlled through various techniques, the situation for bulk crystals beyond laborious chemical doping poses significant challenges. Here, we report the meV-level ultra-fine-tuning of the Fermi level of bulk topological Weyl semimetal TaP using accelerator-based high-energy hydrogen implantation and theory-driven planning. By calculating the desired carrier density and controlling the accelerator profiles, the Fermi level can be fine-tuned from 5 meV to only $\sim$0.5 meV (DFT calculations) away from the Weyl nodes. The Weyl nodes are preserved, while the carrier mobility is largely retained. Our work demonstrates the viability of this generic approach to tune the Fermi level in semimetal systems and could serve to achieve property fine-tuning for other bulk quantum materials with ultrahigh precision.

Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (non-universal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSC, focusing on how a system is identified as a TSC candidate, and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates., Comment: 42 pages, 6 figures

The structure-property relationship plays a central role in materials science. Understanding the structure-property relationship in solid-state materials is crucial for structure design with optimized properties. The past few years witnessed remarkable progress in correlating structures with properties in crystalline materials, such as machine learning methods and particularly graph neural networks as a natural representation of crystal structures. However, significant challenges remain, including predicting properties with complex unit cells input and material-dependent, variable-length output. Here we present the virtual node graph neural network to address the challenges. By developing three types of virtual node approaches - the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve direct prediction of $\Gamma$-phonon spectra and full dispersion only using atomic coordinates as input. We validate the phonon bandstructures on various alloy systems, and further build a $\Gamma$-phonon database containing over 146,000 materials in the Materials Project. Our work provides an avenue for rapid and high-quality prediction of phonon spectra and bandstructures in complex materials, and enables materials design with superior phonon properties for energy applications. The virtual node augmentation of graph neural networks also sheds light on designing other functional properties with a new level of flexibility., Comment: 40 pages total, 4 main figures + 25 supplementary figures