High-Throughput DFT-Based Discovery of Next Generation Two-Dimensional (2D) Superconductors.

High-throughput density functional theory (DFT) calculations allow for a systematic search for conventional superconductors. With the recent interest in two-dimensional (2D) superconductors, we used a high-throughput workflow to screen over 1000 2D materials in the JARVIS-DFT database and performed electron-phonon coupling calculations, using the McMillan-Allen-Dynes formula to calculate the superconducting transition temperature (Tc) for 165 of them. Of these 165 materials, we identify 34 dynamically stable structures with transition temperatures above 5 K, including materials such as W2N3, NbO2, ZrBrO, TiClO, NaSn2S4, Mg2B4C2, and the previously unreported Mg2B4N2 (Tc = 21.8 K). Finally, we performed experiments to determine the Tc of selected layered superconductors (2H-NbSe2, 2H-NbS2, ZrSiS, FeSe) and discuss the measured results within the context of our DFT results. We aim that the outcome of this workflow can guide future computational and experimental studies of new and emerging 2D superconductors by providing a roadmap of high-throughput DFT data.

MPpredictor: An Artificial Intelligence-Driven Web Tool for Composition-Based Material Property Prediction.

The applications of artificial intelligence, machine learning, and deep learning techniques in the field of materials science are becoming increasingly common due to their promising abilities to extract and utilize data-driven information from available data and accelerate materials discovery and design for future applications. In an attempt to assist with this process, we deploy predictive models for multiple material properties, given the composition of the material. The deep learning models described here are built using a cross-property deep transfer learning technique, which leverages source models trained on large data sets to build target models on small data sets with different properties. We deploy these models in an online software tool that takes a number of material compositions as input, performs preprocessing to generate composition-based attributes for each material, and feeds them into the predictive models to obtain up to 41 different material property values. The material property predictor is available online at http://ai.eecs.northwestern.edu/MPpredictor.

Uncertainty Quantification in Atomistic Modeling of Metals and Its Effect on Mesoscale and Continuum Modeling: A Review.

The design of next-generation alloys through the integrated computational materials engineering (ICME) approach relies on multiscale computer simulations to provide thermodynamic properties when experiments are difficult to conduct. Atomistic methods such as density functional theory (DFT) and molecular dynamics (MD) have been successful in predicting properties of never before studied compounds or phases. However, uncertainty quantification (UQ) of DFT and MD results is rarely reported due to computational and UQ methodology challenges. Over the past decade, studies that mitigate this gap have emerged. These advances are reviewed in the context of thermodynamic modeling and information exchange with mesoscale methods such as the phase-field method (PFM) and calculation of phase diagrams (CALPHAD). The importance of UQ is illustrated using properties of metals, with aluminum as an example, and highlighting deterministic, frequentist, and Bayesian methodologies. Challenges facing routine uncertainty quantification and an outlook on addressing them are also presented.

Convergence and machine learning predictions of Monkhorst-Pack k-points and plane-wave cut-off in high-throughput DFT calculations.

In this work, we developed an automatic convergence procedure for k-points and plane wave cut-off in density functional (DFT) calculations and applied it to more than 30000 materials. The computational framework for automatic convergence can take a user-defined input as a convergence criterion. For k-points, we converged energy per cell (EPC) to 0.001 eV/cell tolerance and compared the results with those obtained using an energy per atom (EPA) convergence criteria of 0.001 eV/atom. From the analysis of our results, we could relate k-point density and plane wave cut-off to material parameters such as density, the slope of bands, number of band-crossings, the maximum plane-wave cut-off used in pseudopotential generation, crystal systems, and the number of unique species in materials. We also identified some material species that would require more careful convergence than others. Moreover, we statistically investigated the dependence of k-points and cutoff on exchange-correlation functionals. We utilized all this data to train machine learning models to predict the k-point line density and plane-wave cut-off for generalized materials. This would provide users with a good starting point towards converged DFT calculations. The code used, and the converged data are available on the following websites: https://jarvis.nist.gov/, and https://github.com/usnistgov/jarvis.

Atom Probe Tomography Analysis of Ag Doping in 2D Layered Material (PbSe)5(Bi2Se3)3.

Impurity doping in two-dimensional (2D) materials can provide a route to tuning electronic properties, so it is important to be able to determine the distribution of dopant atoms within and between layers. Here we report the tomographic mapping of dopants in layered 2D materials with atomic sensitivity and subnanometer spatial resolution using atom probe tomography (APT). APT analysis shows that Ag dopes both Bi2Se3 and PbSe layers in (PbSe)5(Bi2Se3)3, and correlations in the position of Ag atoms suggest a pairing across neighboring Bi2Se3 and PbSe layers. Density functional theory (DFT) calculations confirm the favorability of substitutional doping for both Pb and Bi and provide insights into the observed spatial correlations in dopant locations.

Systematic DFT+U and Quantum Monte Carlo Benchmark of Magnetic Two-Dimensional (2D) CrX3 (X = I, Br, Cl, F).

The search for two-dimensional (2D) magnetic materials has attracted a great deal of attention because of the experimental synthesis of 2D CrI3, which has a measured Curie temperature of 45 K. Often times, these monolayers have a higher degree of electron correlation and require more sophisticated methods beyond density functional theory (DFT). Diffusion Monte Carlo (DMC) is a correlated electronic structure method that has been demonstrated to be successful for calculating the electronic and magnetic properties of a wide variety of 2D and bulk systems, since it has a weaker dependence on the Hubbard parameter (U) and density functional. In this study, we designed a workflow that combines DFT +U and DMC in order to treat 2D correlated magnetic systems. We chose monolayer CrX3 (X = I, Br, Cl, F), with a stronger focus on CrI3 and CrBr3, as a case study due to the fact that they have been experimentally realized and have a finite critical temperature. With this DFT+U and DMC workflow and the analytical method of Torelli and Olsen, we estimated a maximum value of 43.56 K for the Tc of CrI3 and 20.78 K for the Tc of CrBr3, in addition to analyzing the spin densities and magnetic properties with DMC and DFT+U. We expect that running this workflow for a well-known material class will aid in the future discovery and characterization of lesser known and more complex correlated 2D magnetic materials.

Computational Methods for Charge Density Waves in 2D Materials.

Two-dimensional (2D) materials that exhibit charge density waves (CDWs)-spontaneous reorganization of their electrons into a periodic modulation-have generated many research endeavors in the hopes of employing their exotic properties for various quantum-based technologies. Early investigations surrounding CDWs were mostly focused on bulk materials. However, applications for quantum devices require few-layer materials to fully utilize the emergent phenomena. The CDW field has greatly expanded over the decades, warranting a focus on the computational efforts surrounding them specifically in 2D materials. In this review, we cover ground in the following relevant theory-driven subtopics for TaS2 and TaSe2: summary of general computational techniques and methods, resulting atomic structures, the effect of electron-phonon interaction of the Raman scattering modes, the effects of confinement and dimensionality on the CDW, and we end with a future outlook. Through understanding how the computational methods have enabled incredible advancements in quantum materials, one may anticipate the ever-expanding directions available for continued pursuit as the field brings us through the 21st century.

Uncertainty Prediction for Machine Learning Models of Material Properties.

Uncertainty quantification in artificial intelligence (AI)-based predictions of material properties is of immense importance for the success and reliability of AI applications in materials science. While confidence intervals are commonly reported for machine learning (ML) models, prediction intervals, i.e., the evaluation of the uncertainty on each prediction, are not as frequently available. In this work, we compare three different approaches to obtain such individual uncertainty, testing them on 12 ML-physical properties. Specifically, we investigated using the quantile loss function, machine learning the prediction intervals directly, and using Gaussian processes. We identify each approach's advantages and disadvantages and end up slightly favoring the modeling of the individual uncertainties directly, as it is the easiest to fit and, in most of the cases, minimizes over- and underestimation of the predicted errors. All data for training and testing were taken from the publicly available JARVIS-DFT database, and the codes developed for computing the prediction intervals are available through the JARVIS-tools package.

Cross-property deep transfer learning framework for enhanced predictive analytics on small materials data.

Artificial intelligence (AI) and machine learning (ML) have been increasingly used in materials science to build predictive models and accelerate discovery. For selected properties, availability of large databases has also facilitated application of deep learning (DL) and transfer learning (TL). However, unavailability of large datasets for a majority of properties prohibits widespread application of DL/TL. We present a cross-property deep-transfer-learning framework that leverages models trained on large datasets to build models on small datasets of different properties. We test the proposed framework on 39 computational and two experimental datasets and find that the TL models with only elemental fractions as input outperform ML/DL models trained from scratch even when they are allowed to use physical attributes as input, for 27/39 (≈ 69%) computational and both the experimental datasets. We believe that the proposed framework can be widely useful to tackle the small data challenge in applying AI/ML in materials science.

Examining Experimental Raman Mode Behavior in Mono- and Bilayer 2H-TaSe2 via Density Functional Theory: Implications for Quantum Information Science.

Tantalum diselenide (TaSe2) is a metallic transition metal dichalcogenide whose structure and vibrational behavior strongly depend on temperature and thickness, and this behavior includes the emergence of charge density wave (CDW) states at very low temperatures. In this work, observed Raman modes for mono- and bilayer are described across several spectral regions and compared to those seen in the bulk case. These modes, which include an experimentally observed forbidden Raman mode and low-frequency CDWs, are then matched to corresponding vibrations predicted by density functional theory (DFT). The reported match between experimental and computational results supports the presented vibrational visualizations of these modes. Support is also provided by experimental phonons observed in additional Raman spectra as a function of temperature and thickness. These results highlight the importance of understanding CDWs since they are likely to play a fundamental role in the future realization of solid-state quantum information platforms based on nonequilibrium phenomena.

Computational scanning tunneling microscope image database.

We introduce the systematic database of scanning tunneling microscope (STM) images obtained using density functional theory (DFT) for two-dimensional (2D) materials, calculated using the Tersoff-Hamann method. It currently contains data for 716 exfoliable 2D materials. Examples of the five possible Bravais lattice types for 2D materials and their Fourier-transforms are discussed. All the computational STM images generated in this work are made available on the JARVIS-STM website ( https://jarvis.nist.gov/jarvisstm ). We find excellent qualitative agreement between the computational and experimental STM images for selected materials. As a first example application of this database, we train a convolution neural network model to identify the Bravais lattice from the STM images. We believe the model can aid high-throughput experimental data analysis. These computational STM images can directly aid the identification of phases, analyzing defects and lattice-distortions in experimental STM images, as well as be incorporated in the autonomous experiment workflows.

Data-driven discovery of 3D and 2D thermoelectric materials.

In this work, we first perform a systematic search for high-efficiency three-dimensional (3D) and two-dimensional (2D) thermoelectric materials by combining semiclassical transport techniques with density functional theory (DFT) calculations and then train machine-learning models on the thermoelectric data. Out of 36 000 three-dimensional and 900 two-dimensional materials currently in the publicly available JARVIS-DFT database, we identify 2932 3D and 148 2D promising thermoelectric materials using a multi-steps screening procedure, where specific thresholds are chosen for key quantities like bandgaps, Seebeck coefficients and power factors. We compute the Seebeck coefficients for all the materials currently in the database and validate our calculations by comparing our results, for a subset of materials, to experimental and existing computational datasets. We also investigate the effect of chemical, structural, crystallographic and dimensionality trends on thermoelectric performance. We predict several classes of efficient 3D and 2D materials such as Ba(MgX)2 (X = P, As, Bi), X2YZ6 (X = K, Rb, Y=Pd, Pt, Z = Cl, Br), K2PtX2 (X = S, Se), NbCu3X4 (X = S, Se, Te), Sr2XYO6 (X = Ta, Zn, Y=Ga, Mo), TaCu3X4 (X = S, Se, Te), and XYN (X = Ti, Zr, Y=Cl, Br). Finally, as high-throughput DFT is computationally expensive, we train machine learning models using gradient boosting decision trees and classical force-field inspired descriptors for n-and p-type Seebeck coefficients and power factors, to quickly pre-screen materials for guiding the next set of DFT calculations. The dataset and tools are made publicly available at the websites: https://www.ctcms.nist.gov/~knc6/JVASP.html, https://www.ctcms.nist.gov/jarvisml/and https://jarvis.nist.gov/.

Author Correction: Enhancing materials property prediction by leveraging computational and experimental data using deep transfer learning.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

High-throughput Discovery of Topologically Non-trivial Materials using Spin-orbit Spillage.

We present a novel methodology to identify topologically non-trivial materials based on band inversion induced by spin-orbit coupling (SOC) effect. Specifically, we compare the density functional theory (DFT) based wavefunctions with and without spin-orbit coupling and compute the 'spin-orbit-spillage' as a measure of band-inversion. Due to its ease of calculation, without any need for symmetry analysis or dense k-point interpolation, the spillage is an excellent tool for identifying topologically non-trivial materials. Out of 30000 materials available in the JARVIS-DFT database, we applied this methodology to more than 4835 non-magnetic materials consisting of heavy atoms and low bandgaps. We found 1868 candidate materials with high-spillage (using 0.5 as a threshold). We validated our methodology by carrying out conventional Wannier-interpolation calculations for 289 candidate materials. We demonstrate that in addition to Z2 topological insulators, this screening method successfully identified many semimetals and topological crystalline insulators. Importantly, our approach is applicable to the investigation of disordered or distorted as well as magnetic materials, because it is not based on symmetry considerations. We discuss some individual example materials, as well as trends throughout our dataset, which is available at the websites: https://www.ctcms.nist.gov/~knc6/JVASP.html and https://jarvis.nist.gov/ .

Accelerated Discovery of Efficient Solar-cell Materials using Quantum and Machine-learning Methods.

Solar-energy plays an important role in solving serious environmental problems and meeting high-energy demand. However, the lack of suitable materials hinders further progress of this technology. Here, we present the largest inorganic solar-cell material search to date using density functional theory (DFT) and machine-learning approaches. We calculated the spectroscopic limited maximum efficiency (SLME) using Tran-Blaha modified Becke-Johnson potential for 5097 non-metallic materials and identified 1997 candidates with an SLME higher than 10%, including 934 candidates with suitable convex-hull stability and effective carrier mass. Screening for 2D-layered cases, we found 58 potential materials and performed G0W0 calculations on a subset to estimate the prediction-uncertainty. As the above DFT methods are still computationally expensive, we developed a high accuracy machine learning model to pre-screen efficient materials and applied it to over a million materials. Our results provide a general framework and universal strategy for the design of high-efficiency solar cell materials. The data and tools are publicly distributed at: https://www.ctcms.nist.gov/~knc6/JVASP.html, https://www.ctcms.nist.gov/jarvisml/, https://jarvis.nist.gov/ and https://github.com/usnistgov/jarvis.

Enhancing materials property prediction by leveraging computational and experimental data using deep transfer learning.

The current predictive modeling techniques applied to Density Functional Theory (DFT) computations have helped accelerate the process of materials discovery by providing significantly faster methods to scan materials candidates, thereby reducing the search space for future DFT computations and experiments. However, in addition to prediction error against DFT-computed properties, such predictive models also inherit the DFT-computation discrepancies against experimentally measured properties. To address this challenge, we demonstrate that using deep transfer learning, existing large DFT-computational data sets (such as the Open Quantum Materials Database (OQMD)) can be leveraged together with other smaller DFT-computed data sets as well as available experimental observations to build robust prediction models. We build a highly accurate model for predicting formation energy of materials from their compositions; using an experimental data set of [Formula: see text] observations, the proposed approach yields a mean absolute error (MAE) of [Formula: see text] eV/atom, which is significantly better than existing machine learning (ML) prediction modeling based on DFT computations and is comparable to the MAE of DFT-computation itself.

Phonon origin and lattice evolution in charge density wave states.

Metallic transition metal dichalcogenides, such as tantalum diselenide (TaSe2), display quantum correlated phenomena of superconductivity and charge density waves (CDW) at low temperatures. Here, the photophysics of 2H-TaSe2 during CDW transitions is revealed by combining temperature-dependent, low-frequency Raman spectroscopy and density functional theory (DFT). The spectra contain amplitude, phase, and zone-folded modes that are assigned to specific phonons and lattice restructuring predicted by DFT calculations with superb agreement. The non-invasive and efficient optical methodology detailed here demonstrates an essential link between atomic-scale and microscopic quantum phenomena.

Materials Science in the AI age: high-throughput library generation, machine learning and a pathway from correlations to the underpinning physics.

The use of advanced data analytics and applications of statistical and machine learning approaches ('AI') to materials science is experiencing explosive growth recently. In this prospective, we review recent work focusing on generation and application of libraries from both experiment and theoretical tools, across length scales. The available library data both enables classical correlative machine learning, and also opens the pathway for exploration of underlying causative physical behaviors. We highlight the key advances facilitated by this approach, and illustrate how modeling, macroscopic experiments and atomic-scale imaging can be combined to dramatically accelerate understanding and development of new material systems via a statistical physics framework. These developments point towards a data driven future wherein knowledge can be aggregated and used collectively, accelerating the advancement of materials science.

Machine learning with force-field inspired descriptors for materials: fast screening and mapping energy landscape.

We present a complete set of chemo-structural descriptors to significantly extend the applicability of machine-learning (ML) in material screening and mapping energy landscape for multicomponent systems. These new descriptors allow differentiating between structural prototypes, which is not possible using the commonly used chemical-only descriptors. Specifically, we demonstrate that the combination of pairwise radial, nearest neighbor, bond-angle, dihedral-angle and core-charge distributions plays an important role in predicting formation energies, bandgaps, static refractive indices, magnetic properties, and modulus of elasticity for three-dimensional (3D) materials as well as exfoliation energies of two-dimensional (2D) layered materials. The training data consists of 24549 bulk and 616 monolayer materials taken from JARVIS-DFT database. We obtained very accurate ML models using gradient boosting algorithm. Then we use the trained models to discover exfoliable 2D-layered materials satisfying specific property requirements. Additionally, we integrate our formation energy ML model with a genetic algorithm for structure search to verify if the ML model reproduces the DFT convex hull. This verification establishes a more stringent evaluation metric for the ML model than what commonly used in data sciences. Our learnt model is publicly available on the JARVIS-ML website (https://www.ctcms.nist.gov/jarvisml) property predictions of generalized materials.

Elastic properties of bulk and low-dimensional materials using Van der Waals density functional.

In this work, we present a high-throughput first-principles study of elastic properties of bulk and monolayer materials mainly using the vdW-DF-optB88 functional. We discuss the trends on the elastic response with respect to changes in dimensionality. We identify a relation between exfoliation energy and elastic constants for layered materials that can help to guide the search for vdW bonding in materials. We also predicted a few novel materials with auxetic behavior. The uncertainty in structural and elastic properties due to the inclusion of vdW interactions is discussed. We investigated 11,067 bulk and 257 monolayer materials. Lastly, we found that the trends in elastic constants for bulk and their monolayer counterparts can be very different. All the computational results are made publicly available at easy-to-use websites: https://www.ctcms.nist.gov/~knc6/JVASP.html and https://jarvis.nist.gov/. Our dataset can be used to identify stiff and flexible materials for industrial applications.