Computational 2D Materials Database Research Articles

Orbital magnetization in two-dimensional materials from high-throughput computational screening

Abstract We calculate the orbital magnetization of 822 two-dimensional magnetic materials from the Computational 2D Materials Database (C2DB). For compounds containing 5$d$ elements we find orbital moments of the order of 0.3--0.5 $\mu_\mathrm{B}$, which points to the necessity of including these in any type of magnetic modeling and comparison with experiments. It is also shown that the alignment of orbital moments with respect to the spin largely follows the predictions from Hund's rule and that deviations may be explained by the $d$-band splitting originating from the crystal field - for example in the important case of CrI$_3$. Finally, we show that for certain insulators, Hubbard corrections may lead to large and fully unquenched orbital moments that are pinned to the lattice rather than the spin and that these moments can lead to enormous magnetic anisotropies. Such unquenched ground states are only found from density functional theory calculations that include both Hubbard corrections and self-consistent spin--orbit coupling and largely invalidates the use of the magnetic force theorem for calculating magnetic anisotropies.

Magnetic order in the computational 2D materials database (C2DB) from high throughput spin spiral calculations

We report high throughput computational screening for magnetic ground state order in 2D materials. The workflow is based on spin spiral calculations and yields the magnetic order in terms of a two-dimensional ordering vector Q. We then include spin-orbit coupling to extract the easy and hard axes for collinear structures and the orientation of spiral planes in non-collinear structures. Finally, for all predicted ferromagnets we compute the Dzyaloshinskii-Moriya interactions and determine whether or not these are strong enough to overcome the magnetic anisotropy and stabilise a chiral spin spiral ground state. We find 58 ferromagnets, 21 collinear anti-ferromagnets, and 85 non-collinear ground states of which 15 are chiral spin spirals driven by Dzyaloshinskii-Moriya interactions. The results show that non-collinear order is in fact as common as collinear order in these materials and emphasise the need for detailed investigation of the magnetic ground state when reporting magnetic properties of new materials.

Ab initio property characterisation of thousands of previously unexplored 2D materials

We perform extensive density functional theory calculations to determine the stability and elementary properties of 4249 previously unexplored monolayer crystals. The monolayers comprise the most stable subset (energy within 0.1 eV/atom of the convex hull) of a larger portfolio of two-dimensional (2D) materials recently discovered using a deep generative model and systematic lattice decoration schemes. The relaxed 2D structures are run through the basic property workflow of the Computational 2D Materials Database (C2DB) to evaluate the dynamical stability and obtain the stiffness tensor, piezoelectric tensor, deformation potentials, Born and Bader charges, electronic band structure, effective masses, plasma frequency, Fermi surface, projected density of states, magnetic moments, magnetic exchange couplings, magnetic anisotropy, topological indices, optical- and infrared polarisability. We provide statistical overviews of the property data and highlight a few specific examples of interesting materials. Our work exposes previously unknown parts of the 2D chemical space and provides a basis for the discovery of 2D materials with specific properties. All data is available in the C2DB.

Two-dimensional altermagnets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects

We present a high throughput computational search for altermagnetism in two-dimensional (2D) materials based on the Computational 2D Materials Database (C2DB). We start by showing that the symmetry requirements for altermagnetism in 2D are somewhat more strict compared to bulk materials and applying these yields a total of seven altermagnets in the C2DB. The collinear ground state in these monolayers is verified by spin spiral calculations using the generalized Bloch theorem. We focus on four d-wave altermagnetic materials belonging to the P21′/c′ magnetic space group—RuF4, VF4, AgF2, and OsF4. The first three of these are known experimentally as van der Waals bonded bulk materials and are likely to be exfoliable from their bulk parent compounds. We perform a detailed analysis of the electronic structure and non-relativistic spin splitting in k-space exemplified by RuF4. The magnon spectrum of RuF4 is calculated from the magnetic force theorem, and it is shown that the symmetries that enforce degenerate magnon bands in anti-ferromagnets are absent in altermagnets and give rise to the non-degenerate magnon spectrum. We then include spin–orbit effects and show that these will dominate the splitting of magnons in RuF4. Finally, we provide an example of i-wave altermagnetism in the 2H-phase of FeBr3.

Symmetry classification of 2D materials: layer groups versus space groups

The symmetry of a crystal structure with a three-dimensional (3D) lattice can be classified by one of the 230 space group types. For some types of crystals, e.g. crystalline films, surfaces, or planar interfaces, it is more appropriate to assume a two-dimensional (2D) lattice. With this assumption the structure can be classified by one of the 80 layer group types. We have implemented an algorithm to determine the layer group type of a 3D structure with a 2D lattice, and applied it to more than 15 000 monolayer structures in the Computational 2D Materials Database (C2DB). We compare the classification of monolayers by layer groups and space groups, respectively. The latter is defined as the space group of the 3D bulk structure obtained by repeating the monolayer periodically in the direction perpendicular to the 2D lattice (AA-stacking). By this correspondence, nine pairs of layer group types are mapped to the same space group type due to the inability of the space group to distinguish the in-plane and out-of-plane axes. In total 18% of the monolayers in the C2DB belong to one of these layer group pairs and are thus not properly classified by the space group type. Our results show that symmetry classification of 2D materials should be based on layer groups rather than the commonly used space groups.

Two-dimensional Materials AlSI, AlSeBr, AlSeI, ScSI, ScSeBr, ScSeCl, ScSeI and InSI for Photocatalytic Water Splitting under Visible Light

This article aims to investigate possible 2D photocatalysts for water splitting and to provide a comprehensive overview of some selected candidate materials from the Computational 2D Materials Database (C2DB). In this article, several 2D materials that have not yet been synthesized or investigated are reviewed. The structure, electronic and optical properties were investigated for many materials, taking into account some criteria for the selection of candidates, such as ABC materials from groups 6 and 7, a band gap of 1.6 to 2.8 eV by HSE calculation, and that these monolayers should be non-magnetic. In this article, it was found that AlSI, AlSeBr, AlSeI, ScSI, ScSeBr, ScSeCl, ScSeI, and InSI (the space groups of these materials are Pmmn (No. 59)) can be used for photocatalytic water splitting. These materials were dynamically stable and possessed excellent visible light absorption. The calculated band gaps were between 2.2 and 2.8 eV and their edge positions of CBM and VBM perfectly matched the oxidation and reduction potentials of water.

Structural and Electronic Properties of Two-Dimensional Materials: A Machine-Learning-Guided Prediction.

The growing number of studies and interest in two-dimensional (2D) materials has not yet resulted in a wide range of material applications. This is a result of difficulties in getting the properties, which are often determined through numerical experiments or through first-principles predictions, both of which require lots of time and resources. Here we provide a general machine learning (ML) model that works incredibly well as a predictor for a variety of electronic and structural properties such as band gap, fermi level, work function, total energy and area of unit cell for a wide range of 2D materials derived from the Computational 2D Materials Database (C2DB). Our predicted model for classification of samples works extraordinarily well and gives an accuracy of around 99 %. We are able to successfully decrease the number of studied features by employing a strict permutation-based feature selection method along with the sure independence screening and sparsifying operator (SISSO), which further supports the design recommendations for the identification of novel 2D materials with the desired properties.

Predicting the work function of 2D MXenes using machine-learning methods

MXenes, which are graphene-like two-dimensional transition metal carbides and nitrides, have tunable compositions and exhibit rich surface chemistry. This compositional flexibility has resulted in exquisitely tunable electronic, optical, and mechanical properties leading to the applications of MXenes in catalysis, electronics, and energy storage. The work function of MXenes is an important fundamental property that dictates the suitability of MXenes for these applications. We present a series of machine learning models to predict the work function of MXenes having generic compositions and containing surfaces terminated by O*, OH*, F*, and bare metal atoms. Our model uses the basic chemical properties of the elements constituting the MXene as features, and is trained on 275 data points from the Computational 2D Materials Database. Using 15 different features of the MXene as inputs, the neural network model predicts the work function of MXenes with a mean absolute error of 0.12 eV on the training data and 0.25 eV on the testing data. Our feature importance analysis indicates that properties of atoms terminating the MXene surface like their electronegativity, most strongly influence the work function. This sensitivity of the work function to the surface termination is also elucidated through experimental measurements on Ti3C2. We introduce reduced-order models comprising of ten-, eight-, and five-features to predict the work function. These reduced-order models exhibit easier transferability to new materials, while exhibiting a marginal increased mean average error. We demonstrate the transferability of these reduced order models to new materials, by predicting the work function of MXenes having surface terminations beyond the original training set, like Br*, Cl*, S*, N*, and NH*. Predicting electronic properties like the work function from the basic chemical properties of elements, paves the way towards rapidly identifying tailored MXenes having a targeted range of properties that are required for a specific application.

Two-dimensional ferroelectrics from high throughput computational screening

We report a high throughput computational search for two-dimensional ferroelectric materials. The starting point is 252 pyroelectric materials from the computational 2D materials database (C2DB) and from these we identify 63 ferroelectrics. In particular we find 49 materials with in-plane polarization, 8 materials with out-of-plane polarization and 6 materials with coupled in-plane and out-of-plane polarization. Most of the known 2D ferroelectrics are recovered by the screening and the far majority of the predicted ferroelectrics are known as bulk van der Waals bonded compounds, which makes them accessible by direct exfoliation. For roughly 25% of the materials we find a metastable state in the non-polar structure, which may imply a first order transition to the polar phase. Finally, we list the magnetic pyroelectrics extracted from the C2DB and focus on the case of VAgP2Se6, which exhibits a three-state switchable polarization vector that is strongly coupled to the magnetic excitation spectrum.

Exploring and machine learning structural instabilities in 2D materials

We address the problem of predicting the zero-temperature dynamical stability (DS) of a periodic crystal without computing its full phonon band structure. Here we report the evidence that DS can be inferred with good reliability from the phonon frequencies at the center and boundary of the Brillouin zone (BZ). This analysis represents a validation of the DS test employed by the Computational 2D Materials Database (C2DB). For 137 dynamically unstable 2D crystals, we displace the atoms along an unstable mode and relax the structure. This procedure yields a dynamically stable crystal in 49 cases. The elementary properties of these new structures are characterized using the C2DB workflow, and it is found that their properties can differ significantly from those of the original unstable crystals, e.g., band gaps are opened by 0.3 eV on average. All the crystal structures and properties are available in the C2DB. Finally, we train a classification model on the DS data for 3295 2D materials in the C2DB using a representation encoding the electronic structure of the crystal. We obtain an excellent receiver operating characteristic (ROC) curve with an area under the curve (AUC) of 0.90, showing that the classification model can drastically reduce computational efforts in high-throughput studies.

Computational screening of two-dimensional substrates for stabilizing honeycomb borophene

Honeycomb borophene (hc-B) has received extensive attention due to its potential applications in energy storage, sensors, and superconductivity. However, due to the indecisive kinetic and thermodynamic stability of the freestanding hc-B, its further development is limited. To enhance the stability of hc-B, the substrates engineering is more straightforward and feasible in practice without changing the intrinsic hc-B structure. Herein, steered via first-principle calculations, we perform a computational screening of two-dimensional (2D) substrates for stabilizing the hc-B from the Computational 2D Materials Database. Consequently, we find 8 new candidates with improved stability, whose structural integrity of hc-B is well-maintained. The strong interactions between the hc-B and the substrates play a critical role in the stability enhancement, confirmed by the large binding energy and charge transfer. In addition, the preferential migration pathway of boron atoms on the substrates is restricted by the potential energy surface, benefiting the epitaxial growth of hc-B. Our results suggest that the 2D layered substrates are promising for stabilizing and growing planar hc-B structure, which may facilitate its applications in 2D fields.

Data-driven discovery of 2D materials by deep generative models

Efficient algorithms to generate candidate crystal structures with good stability properties can play a key role in data-driven materials discovery. Here, we show that a crystal diffusion variational autoencoder (CDVAE) is capable of generating two-dimensional (2D) materials of high chemical and structural diversity and formation energies mirroring the training structures. Specifically, we train the CDVAE on 2615 2D materials with energy above the convex hull ΔHhull < 0.3 eV/atom, and generate 5003 materials that we relax using density functional theory (DFT). We also generate 14192 new crystals by systematic element substitution of the training structures. We find that the generative model and lattice decoration approach are complementary and yield materials with similar stability properties but very different crystal structures and chemical compositions. In total we find 11630 predicted new 2D materials, where 8599 of these have ΔHhull < 0.3 eV/atom as the seed structures, while 2004 are within 50 meV of the convex hull and could potentially be synthesised. The relaxed atomic structures of all the materials are available in the open Computational 2D Materials Database (C2DB). Our work establishes the CDVAE as an efficient and reliable crystal generation machine, and significantly expands the space of 2D materials.

Reconstructing the exit wave of 2D materials in high-resolution transmission electron microscopy using machine learning

Reconstruction of the exit wave function is an important route to interpreting high-resolution transmission electron microscopy (HRTEM) images. Here we demonstrate that convolutional neural networks can be used to reconstruct the exit wave from a short focal series of HRTEM images, with a fidelity comparable to conventional exit wave reconstruction. We use a fully convolutional neural network based on the U-Net architecture, and demonstrate that we can train it on simulated exit waves and simulated HRTEM images of graphene-supported molybdenum disulphide (an industrial desulfurization catalyst). We then apply the trained network to analyse experimentally obtained images from similar samples, and obtain exit waves that clearly show the atomically resolved structure of both the MoS2 nanoparticles and the graphene support. We also show that it is possible to successfully train the neural networks to reconstruct exit waves for 3400 different two-dimensional materials taken from the Computational 2D Materials Database of known and proposed two-dimensional materials.

Density-of-states similarity descriptor for unsupervised learning from materials data

We develop a materials descriptor based on the electronic density-of-states (DOS) and investigate the similarity of materials based on it. As an application example, we study the Computational 2D Materials Database (C2DB) that hosts thousands of two-dimensional materials with their properties calculated by density-functional theory. Combining our descriptor with a clustering algorithm, we identify groups of materials with similar electronic structure. We introduce additional descriptors to characterize these clusters in terms of crystal structures, atomic compositions, and electronic configurations of their members. This allows us to rationalize the found (dis)similarities and to perform an automated exploratory and confirmatory analysis of the C2DB data. From this analysis, we find that the majority of clusters consist of isoelectronic materials sharing crystal symmetry, but we also identify outliers, i.e., materials whose similarity cannot be explained in this way.

Quantum point defects in 2D materials - the QPOD database

Atomically thin two-dimensional (2D) materials are ideal host systems for quantum defects as they offer easier characterisation, manipulation and read-out of defect states as compared to bulk defects. Here we introduce the Quantum Point Defect (QPOD) database with more than 1900 defect systems comprising various charge states of 503 intrinsic point defects (vacancies and antisites) in 82 different 2D semiconductors and insulators. The Atomic Simulation Recipes (ASR) workflow framework was used to perform density functional theory (DFT) calculations of defect formation energies, charge transition levels, Fermi level positions, equilibrium defect and carrier concentrations, transition dipole moments, hyperfine coupling, and zero-field splitting. Excited states and photoluminescence spectra were calculated for selected high-spin defects. In this paper we describe the calculations and workflow behind the QPOD database, present an overview of its content, and discuss some general trends and correlations in the data. We analyse the degree of defect tolerance as well as intrinsic dopability of the host materials and identify promising defects for quantum technological applications. The database is freely available and can be browsed via a web-app interlinked with the Computational 2D Materials Database (C2DB).

Bandgap prediction of two-dimensional materials using machine learning.

The bandgap of two-dimensional (2D) materials plays an important role in their applications to various devices. For instance, the gapless nature of graphene limits the use of this material to semiconductor device applications, whereas the indirect bandgap of molybdenum disulfide is suitable for electrical and photo-device applications. Therefore, predicting the bandgap rapidly and accurately for a given 2D material structure has great scientific significance in the manufacturing of semiconductor devices. Compared to the extremely high computation cost of conventional first-principles calculations, machine learning (ML) based on statistics may be a promising alternative to predicting bandgaps. Although ML algorithms have been used to predict the properties of materials, they have rarely been used to predict the properties of 2D materials. In this study, we apply four ML algorithms to predict the bandgaps of 2D materials based on the computational 2D materials database (C2DB). Gradient boosted decision trees and random forests are more effective in predicting bandgaps of 2D materials with an R2 >90% and root-mean-square error (RMSE) of ~0.24 eV and 0.27 eV, respectively. By contrast, support vector regression and multi-layer perceptron show that R2 is >70% with RMSE of ~0.41 eV and 0.43 eV, respectively. Finally, when the bandgap calculated without spin-orbit coupling (SOC) is used as a feature, the RMSEs of the four ML models decrease greatly to 0.09 eV, 0.10 eV, 0.17 eV, and 0.12 eV, respectively. The R2 of all the models is >94%. These results show that the properties of 2D materials can be rapidly obtained by ML prediction with high precision.

Recent progress of the Computational 2D Materials Database (C2DB)

The Computational 2D Materials Database (C2DB) is a highly curated open database organising a wealth of computed properties for more than 4000 atomically thin two-dimensional (2D) materials. Here we report on new materials and properties that were added to the database since its first release in 2018. The set of new materials comprise several hundred monolayers exfoliated from experimentally known layered bulk materials, (homo)bilayers in various stacking configurations, native point defects in semiconducting monolayers, and chalcogen/halogen Janus monolayers. The new properties include exfoliation energies, Bader charges, spontaneous polarisations, Born charges, infrared polarisabilities, piezoelectric tensors, band topology invariants, exchange couplings, Raman spectra and second harmonic generation spectra. We also describe refinements of the employed material classification schemes, upgrades of the computational methodologies used for property evaluations, as well as significant enhancements of the data documentation and provenance. Finally, we explore the performance of Gaussian process-based regression for efficient prediction of mechanical and electronic materials properties. The combination of open access, detailed documentation, and extremely rich materials property data sets make the C2DB a unique resource that will advance the science of atomically thin materials.

Two-Dimensional Materials with Giant Optical Nonlinearities near the Theoretical Upper Limit.

Nonlinear optical (NLO) phenomena such as harmonic generation and Kerr and Pockels effects are of great technological importance for lasers, frequency converters, modulators, switches, etc. Recently, two-dimensional (2D) materials have drawn significant attention due to their strong and peculiar NLO properties. Here, we describe an efficient first-principles workflow for calculating the quadratic optical response and apply it to 375 non-centrosymmetric semiconductor monolayers from the Computational 2D Materials Database (C2DB). Sorting the nonresonant nonlinearities with respect to bandgap Eg reveals an upper limit proportional to Eg-4, which is neatly explained by two distinct generic models. We identify multiple promising candidates with giant nonlinearities and bandgaps ranging from 0.4 to 5 eV, some of which approach the theoretical upper limit and greatly outperform known materials. Our comprehensive library of ab initio NLO spectra for all 375 monolayers is freely available via the C2DB Web site.

A library of ab initio Raman spectra for automated identification of 2D materials

Raman spectroscopy is frequently used to identify composition, structure and layer thickness of 2D materials. Here, we describe an efficient first-principles workflow for calculating resonant first-order Raman spectra of solids within third-order perturbation theory employing a localized atomic orbital basis set. The method is used to obtain the Raman spectra of 733 different monolayers selected from the Computational 2D Materials Database (C2DB). We benchmark the computational scheme against available experimental data for 15 known monolayers. Furthermore, we propose an automatic procedure for identifying a material based on an input experimental Raman spectrum and apply it to the cases of MoS2 (H-phase) and WTe2 (T{}^{prime}-phase). The Raman spectra of all materials at different excitation frequencies and polarization configurations are freely available from the C2DB. Our comprehensive and easily accessible library of ab initio Raman spectra should be valuable for both theoreticians and experimentalists in the field of 2D materials.

Computational screening of two-dimensional coatings for semiconducting photocathodes

Alkali-based semiconducting photocathodes, due to their high quantum efficiency (QE) in the visible light spectrum, are promising candidates to replace traditional metal photocathodes for high-brightness beam applications such as x-ray free electron lasers (XFELs). However, they suffer from rapid degradation which significantly limits their operational lifetimes. Coating them with two-dimensional (2D) materials has been proposed as a possible avenue to prevent the degradation. Ideally, the 2D coating layer should not increase the work function of semiconducting photocathodes, thus maintaining the high QE of semiconducting photocathodes in visible light. Herein, we report a computational screening of over 4000 2D materials in the Computational 2D Materials Database (C2DB). The assessment of their potential to be good coating layers is based on their effects to the surface electronic properties. We discover several candidate materials that are even capable of decreasing the work function of semiconducting photocathodes. Some of the experimentally synthesized 2D materials, such as hydrogenated graphene (graphane) and several hydroxylated transition metal carbides/nitrides (MXenes), are particularly appealing for this application.