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The Computational 2D Materials Database: High-Throughput Modeling and Discovery of Atomically Thin Crystals

Sten Haastrup, Mikkel Strange, Mohnish Pandey, Thorsten Deilmann, Per S. Schmidt, Nicki F. Hinsche, Morten N. Gjerding, Daniele Torelli, Peter M. Larsen, Anders C. Riis-Jensen, Jakob Gath, Karsten W. Jacobsen, Jens Jørgen Mortensen, Thomas Olsen, Kristian S. Thygesen

arXiv:1806.03173v2cond-mat.mes-hallcond-mat.mtrl-sci

TL;DR

Existing approaches are not quantitatively accurate for excited-state properties such as electronic band structures and optical absorption spectra. The paper introduces the open Computational 2D Materials Database, identifies potentially synthesisable 2D materials with interesting properties, and provides an open database for calculated two-dimensional-material properties.

  • Problem

    Existing approaches are generally not quantitatively accurate for excited-state properties such as electronic band structures and optical absorption spectra.

  • Method

    The paper introduces the open Computational 2D Materials Database (C2DB), an open database with calculated properties of two-dimensional materials.

  • Results

    The C2DB identified potentially synthesisable 2D materials including ferromagnets with large magnetic anisotropy, semiconductors with high intrinsic carrier mobility, and metals with plasmons in the visible frequency range.

  • Takeaways & Limitations

    The C2DB provides an open database of calculated two-dimensional-material properties for computational modeling and discovery.

  • Takeaways & Limitations

    The database’s underlying approaches are generally not quantitatively accurate for excited-state properties such as electronic band structures and optical absorption spectra.

Abstract

from arXiv · show

We introduce the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than 30 different crystal structures. Material properties are systematically calculated by state-of-the art density functional theory and many-body perturbation theory (G$_0\!$W$\!_0$ and the Bethe-Salpeter Equation for $\sim$200 materials) following a semi-automated workflow for maximal consistency and transparency. The C2DB is fully open and can be browsed online or downloaded in its entirety. In this paper, we describe the workflow behind the database, present an overview of the properties and materials currently available, and explore trends and correlations in the data. Moreover, we identify a large number of new potentially synthesisable 2D materials with interesting properties targeting applications within spintronics, (opto-)electronics, and plasmonics. The C2DB offers a comprehensive and easily accessible overview of the rapidly expanding family of 2D materials and forms an ideal platform for computational modeling and design of new 2D materials and van der Waals heterostructures.

1 Introduction

The C2DB addresses the limited development of computational databases for 2D materials by systematically organizing consistent, open data across broad property classes. It also uses large-scale materials generation and analysis to identify potentially synthesisable monolayers and candidates with targeted electronic, magnetic, optical, and plasmonic properties.

  • Beyond known materials, combinatorial lattice decoration identifies another few hundred previously unknown and potentially synthesisable monolayers.
  • The C2DB organizes ab-initio calculated properties for more than 1500 2D materials, covering structural, thermodynamic, magnetic, elastic, electronic, dielectric, and optical behavior.
  • All materials are evaluated with common codes, parameter settings, and workflows to improve transparency, reproducibility, and consistency.
  • The database is freely accessible online and downloadable, enabling open sharing, comparison, benchmarking, and data-driven materials discovery.
  • More than 1900 monolayers across 32 crystal structures include 350 in the most stable category, around 80 derived from experimentally known layered bulk materials, and around 200 completely new potentially synthesisable materials.
  • The analysis reveals candidate ferromagnets with large magnetic anisotropy, high-mobility semiconductors, and metals with plasmons in the optical or visible frequency range.

2 Workflow

The C2DB workflow generates candidate monolayers, relaxes and filters their structures, then calculates properties for materials meeting stability and geometry criteria. A semi-automated, openly available GPAW–ASE implementation applies documented parameters and convergence checks throughout.

  • Workflow stages: The workflow has an initial structural stage and a subsequent property stage for materials satisfying stability and geometry criteria.The second stage computes properties using DFT and many-body methods; G0W0 and BSE are restricted to semiconductors with up to four atoms per unit cell.
  • Implementation and reproducibility: The workflow is implemented with GPAW and ASE, supported by convergence-verified scripts and a freely available GPL-licensed library.The paper documents numerical parameters and benchmarking for the workflow steps.
  • Structure generation and relaxation: Candidate materials begin from crystal prototypes decorated with selected elements, then undergo unit-cell and internal-coordinate relaxation in NM, FM, and AFM configurations.AFM calculations are performed only for unit cells containing at least two metal atoms.
  • Structural filtering: After relaxation, structural checks retain only materials forming exactly one covalently connected two-dimensional cluster.Connectivity uses covalent radii increased by 30%, and cluster dimensionality is determined from atom-count scaling under unit-cell repetition.
  • Structural filtering: Most candidates have a critical covalent factor below 1.3, while around 100 disconnected materials are excluded from the database.The excluded candidates lie in the red region of the covalent-factor distribution.
  • Validation: Comparison against 29 monolayers gives a mean absolute lattice-constant deviation of 0.024 Å, corresponding to 0.4%.The small finite deviations are attributed to differences in PAW potentials.

2.2 Crystal structure classification

C2DB classifies materials by crystal symmetry, stoichiometry, and comparable thickness, while assessing thermodynamic stability relative to competing bulk phases. The authors caution that convex-hull energies are guidelines rather than direct synthesisability criteria because DFT, substrate, and kinetic effects matter.

  • Crystal structure classification: Materials share a crystal prototype when they have the same space group, stoichiometry, and comparable thicknesses.Thickness distinguishes structures with identical symmetry and stoichiometry but different numbers of atomic layers.
  • Prototypes: Crystal prototypes are labelled by representative materials, including structures outside previously known crystal-structure conventions because C2DB contains never-synthesised materials.Representative materials are selected according to the lowest energy relative to the convex hull when needed.
  • Thermodynamic stability: PBE formation energies have an average accuracy of around 0.2 eV/atom, so hull diagrams should be treated as guidelines.The authors also note that bulk reference energies may be slightly overestimated relative to monolayers because PBE misses attractive van der Waals interactions.
  • Thermodynamic stability: Thermodynamic stability requires energy below the convex hull of all competing phases, not merely a negative heat of formation.C2DB evaluates the 2D material relative to a convex hull constructed from stable bulk compounds.
  • Thermodynamic stability: For 2D materials, convex-hull stability is not a direct synthesisability criterion because DFT energy uncertainty, substrate interactions, and kinetic barriers can stabilize monolayers.These effects can make a monolayer practically metastable despite competing lower-energy phases.
  • Thermodynamic stability: In the Fe–Se example, most 2D materials lie above the convex hull, whereas antiferromagnetic FeSe lies slightly below it and is predicted thermodynamically stable.The FeSe prediction is consistent with experimental observation of AFM order in monolayer FeSe on SrTiO3.

2.4 Phonons and dynamic stability

The workflow assesses dynamical stability using finite-displacement phonons in a 2×2 supercell, while combining phonon and thermodynamic criteria to classify candidate monolayers. The phonon test is necessary but not sufficient because it can miss instabilities at interior Brillouin-zone points.

  • Phonon calculation: Finite displacements of ±0.01 Å generate forces and a dynamical matrix whose eigenvalues provide mass-renormalised phonon-frequency information.Negative eigenvalues correspond to imaginary frequencies and indicate a saddle point.
  • Phonon calculation: The procedure explicitly tests local distortions with periodicities up to 2×2, providing a necessary but not sufficient condition for dynamical stability.A full phonon band structure would be required for a rigorous stability test.
  • Phase stability: The stability analysis compares T and T′ transition-metal dichalcogenide and oxide phases using Γ-point dynamical-matrix eigenvalues and relaxed-structure RMSD.The RMSD identifies cases where relaxations from the two starting phases produce effectively identical structures.
  • Validation against known monolayers: Among known monolayers, all but five have hull energies below 0.2 eV/atom, and all but one have positive minimum dynamical-matrix eigenvalues.Three of the five higher-hull-energy materials were synthesized only on metal substrates.
  • Stability criteria: C2DB materials receive low, medium, or high dynamical and thermodynamic stability levels, with overall stability set by the lower of the two.Medium-stability materials may be metastable and synthesizable under suitable conditions, whereas low overall stability is treated as unstable.

2.5 Elastic constants

The C2DB computes planar elastic stiffness coefficients from stress responses to small relaxed strains. The resulting values agree well with prior PBE calculations and show good numerical consistency for isotropic materials.

  • Tensor formulation: In two dimensions, stress and strain have three independent components, while the stiffness tensor is a symmetric linear map with up to six independent components.The analysis disregards shear deformations when focusing on planar stiffness coefficients.
  • Calculation: The workflow calculates C11, C22, and C12 for every C2DB material using a central-difference approximation.These coefficients describe the planar elastic response.
  • Calculation: ±1% strains are applied after ionic relaxation, large enough to reduce numerical noise while remaining within the linear-response regime.The stress tensor is evaluated after the ions have relaxed.
  • Validation: The calculated planar stiffness values are in very good agreement with previously published PBE results.Table 3 reports the comparison and mean absolute deviation.
  • Validation: For isotropic MoS2, WSe2, and WS2, C11 and C22 vary by up to 0.6%, providing a convergence check.These coefficients should be identical for the isotropic materials.

2.6 Magnetic anisotropy

The database evaluates magnetic anisotropy from energy differences between magnetization directions, while its electronic workflow combines PBE, HSE06, GLLBSC, and selected G0W0 calculations. Comparisons show close agreement with reference calculations and experiments, with systematic methodological caveats.

  • Magnetic anisotropy: Magnetic anisotropy is obtained from energy differences between out-of-plane and in-plane magnetization directions using the magnetic force theorem.Negative in-plane anisotropy energies indicate an out-of-plane easy axis.
  • Electronic structure: Projected density of states identifies contributions from atomic orbitals by species and angular-momentum channel using PAW projectors and linear-tetrahedron interpolation.The method returns exactly zero where no states exist, unlike smeared PDOS techniques.
  • Electronic structure: Band structures are evaluated along high-symmetry paths for five 2D Bravais lattices using PBE, HSE06, GLLBSC, and selected G0W0 calculations with SOC included.G0W0 is applied to finite-gap materials with up to four atoms per unit cell, currently around 250 materials.
  • Validation: 0.041 eV is the mean absolute deviation between C2DB and VASP PBE+SOC band gaps for 29 monolayers.The corresponding HSE+SOC comparison has a 0.14 eV mean absolute deviation.
  • Band gaps: The PBE band gap of WS2 increases from 1.52 eV to 2.05 eV with HSE06, consistent with earlier reported PBE and HSE values.Earlier work reports 1.50 eV and 1.90 eV, and 1.55 eV and 1.98 eV, respectively.
  • G0W0 validation: G0W0 opens the PBE band gap by 1.00 eV and the HSE gap by 0.47 eV, while 51-monolayer TMDC results agree with an independent dataset within 0.1 eV mean absolute error.The G0W0 results are all within 0.2 eV of experiment.

2.9 Band extrema

The database locates the valence-band maximum and conduction-band minimum in the Brillouin zone and reports their energies relative to a consistently defined vacuum level. Dipole corrections account for asymmetric electrostatic potentials in polar monolayers.

  • Band extrema: For finite-gap materials, the workflow identifies the VBM and CBM locations and energies relative to the vacuum level.The vacuum level is defined from the asymptotic electrostatic potential.
  • Vacuum alignment: The PBE electrostatic potential defines the vacuum level used in non-selfconsistent HSE and G0W0 calculations.This keeps band-edge energies referenced to a common potential convention.
  • Validation: The band-edge workflow is paired with convergence checks for quasiparticle gaps and comparisons of calculated and experimental monolayer gaps.Figure 11 examines k-point and plane-wave convergence, while Table 4 reports calculated–experimental comparisons.
  • Vacuum alignment: For out-of-plane dipoles, a dipole correction is applied and the vacuum level is averaged from the asymptotic potentials on both sides.The PBE vacuum-level shift is also stored in the database.

2.10 Fermi surface

The C2DB calculates Fermi surfaces for metallic compounds using PBE with SOC, interpolating eigenvalues within the first Brillouin zone. VO2-MoS2 illustrates spin-resolved Fermi-surface structure in a ferromagnetic state.

  • All metallic compounds receive PBE+SOC Fermi-surface calculations, with eigenvalues quadratically interpolated and plotted within the first Brillouin zone.The workflow uses a ground-state calculation with a k-point density of at least 20/˚A−1.
  • VO2-MoS2 has a ferromagnetic ground state with a magnetic moment of 0.70 µB per unit cell.Its Fermi surface is colored by the out-of-plane spin projection ⟨Sz⟩, showing alternating lobes with ⟨Sz⟩= ±1.

2.11 Effective masses

The C2DB extracts electron, hole, and exciton effective masses from band curvatures, including anisotropy and SOC effects. Examples demonstrate heavy and light directions, SOC splitting, and Rashba-induced conduction-band structure.

  • Effective masses are obtained by fitting third-order polynomials to bands within 100 meV of the VBM or CBM.Diagonalising each band’s mass tensor yields heavy and light masses when curvatures are anisotropic.
  • The database stores masses in two directions and energetic splittings both with and without SOC, using a simple scheme suited to many materials.The approach was chosen for simplicity and ease of application across different materials.
  • The exciton reduced mass is calculated from the curvature of direct valence-conduction transition energies.For direct gaps, it relates to electron and hole masses through 1/µex = 1/m∗.
  • Indirect band gaps do not obey the direct-gap relation between exciton, electron, and hole masses.This is a scope limitation of that relation rather than of the mass calculation itself.
  • SnS-GeSe exhibits anisotropic bands, approximately 10 meV SOC valence-band splitting, and Rashba-related conduction-band splitting.The Rashba effect arises from SOC combined with the finite perpendicular electric field generated by the structure’s permanent dipole, associated with a 1.13 eV vacuum-level difference.
  • C2DB effective masses agree satisfactorily with previously published PBE+SOC data.

2.12 Work function

The database evaluates work functions, deformation potentials, and plasma-frequency-related quantities using consistent first-principles procedures. These calculations support analysis of strain-dependent band edges and plasmon response.

  • 2.12 Work function: For metallic compounds, the work function is the difference between the Fermi energy and the asymptotic vacuum electrostatic potential.It is determined for both PBE and HSE band structures including SOC.
  • 2.13 Deformation potentials: Deformation potentials quantify band-edge shifts under linear lattice deformation and are computed from ±1% uniaxial strain calculations.The band-energy change is measured relative to vacuum, with care required when bands cross under strain.
  • 2.13 Deformation potentials: MoS2 band edges both shift downward under tensile x-strain, but the larger CBM shift produces effective band-gap closing.
  • 2.13 Deformation potentials: Deformation potentials show generally good agreement with literature values, with discrepancies partly attributed to inclusion of SOC.They also estimate acoustic electron-phonon interaction strength and support strain engineering and band-edge uncertainty estimates.

2.15 Electronic polarisability

The C2DB describes 2D dielectric response through the polarisability, calculated within the RPA for in-plane and out-of-plane optical response. Examples distinguish semiconductor absorption onset and metallic intraband contributions.

  • The 2D polarisability is defined from the induced dipole moment per unit area, providing a natural generalisation for atomically thin materials.It is related to the dielectric tensor through αij = (ϵij −δij)/(4π) after appropriate slab integration.
  • The response function follows a Dyson equation, with RPA replacing the irreducible response by the non-interacting response function.
  • Polarisabilities are calculated for all materials in both in-plane and out-of-plane directions in the optical limit q →0.Metallic interband and separately treated intraband contributions are included using PBE eigenvalues and states.
  • MoS2 shows dissipation onset at its 1.6 eV PBE band gap and a static polarisability of approximately 6 Å.The initial constant imaginary polarisability is consistent with a 2D parabolic-band density of states.
  • For metallic 1T-NbS2, the real polarisability is displayed with and without the intraband Drude contribution.

2.16 Optical absorbance

The C2DB computes optical absorption using RPA and BSE methods, with BSE capturing excitonic effects. Calculations agree well with experiments, while convergence and approximation limits affect reported exciton properties.

  • Methods: BSE captures excitonic effects in 2D semiconductor absorption spectra that are absent from RPA.The BSE is described as a method capable of describing excitonic effects and agreeing with experimental absorption spectra.
  • Optical spectra: MoS2 shows a low-energy double exciton peak in the in-plane BSE spectrum, corresponding to A and B excitons.The two peaks are separated by 0.15 eV and originate from valence-band spin-orbit splitting at K.
  • Convergence: 0.53 eV is the MoS2 exciton binding energy at the database’s 48 × 48 k-point sampling, compared with 0.47 eV after extrapolation to infinite sampling.The finite-grid result therefore overestimates the extrapolated value by approximately 0.06 eV.
  • Convergence: Exciton binding energies decrease with increasing k-point sampling, so C2DB values may be slightly overestimated.Electronic-excitation calculations converge slowly because of non-analytic dielectric behavior near q = 0.
  • Convergence: BSE-G0W0 absorption-peak positions converge faster than band gaps or exciton binding energies alone because their k-point errors tend to cancel.Increasing k-point sampling reduces both the G0W0 gap and exciton binding energy, partially offsetting their effects on peak positions.
  • Validation: Calculated first excitonic-peak positions agree well with experimental observations for four TMDC monolayers and phosphorene.Substrate screening can alter exciton properties, but the reported comparison concerns pristine monolayer calculations.

3 Database overview

The database overview examines material distributions, stability, electronic and transport properties, magnetism, plasmons, and excitons. It uses these analyses to identify trends and candidate materials for further study and synthesis.

  • Scope: The overview presents material distributions, basic properties, stability descriptors, and analyses of band gaps, mobility, magnetism, plasmons, and excitons.The analysis is intended to explore trends and correlations rather than provide material-specific studies.
  • Materials: The C2DB includes experimentally synthesized monolayers and additional monolayers that could potentially be exfoliated from known layered materials.The overview also lists materials not experimentally known that are proposed as candidates for further study and synthesis.
  • Stability: Materials with high dynamical stability have a mean energy above the convex hull of 0.12 eV, versus 0.25 eV for other materials.The materials form two clusters according to dynamic stability, and greater dynamic stability is associated with greater thermodynamic stability.
  • Electronic properties: GLLBSC band gaps are on average 2% smaller than G0W0, whereas HSE06 gaps are systematically underestimated by more than 20%.The comparison uses G0W0 as the reference for assessing DFT band-gap methods.
  • Electronic properties: PBE and HSE06 predict qualitatively wrong Type II-to-Type III band alignments in 44% and 21% of cases, respectively, relative to G0W0.PBE systematically underestimates the band offset because it underestimates the band gaps of both monolayers.
  • Effective masses and mobility: The mean electron effective mass is 0.9 m0 and the mean hole effective mass is 1.1 m0, with electron masses below m0 in 80% of cases versus 65% for holes.Electron and hole masses show no clear correlation, although electron masses are generally slightly smaller.
  • Effective masses and mobility: Previously unknown materials fall in the predicted high-mobility region and could be candidates for high-mobility 2D semiconductors.Phosphorene is predicted to have among the highest mobilities for both electrons and holes, consistent with experiments.
  • Magnetism: Halides generally exhibit larger magnetic anisotropies than chalcogenides, with iodine standing out as the most significant element for large anisotropy.Large anisotropy also occurs in several 3d metal iodides, reflecting interplay among spins, orbital hybridisation, and crystal field.

4 Conclusions and Outlook

The C2DB is an open, expanding database of computed properties for more than 1500 two-dimensional materials, generated through a systematic high-throughput workflow. It supports materials discovery, benchmarking, model development, and exploration of heterostructures, while remaining limited by idealized pristine-crystal assumptions and incomplete property coverage.

  • The C2DB is openly browsable and downloadable, with documented parameters and freely available generation scripts supporting transparency and reproducibility.
  • More than 1500 materials across 32 crystal structures are currently included in the C2DB.
  • The database combines structural, elastic, thermodynamic, electronic, magnetic, dielectric, and optical properties computed through a high-throughput, semi-automated workflow.Beyond-DFT methods including GW, RPA, and BSE improve descriptions of band gaps and optical spectra, which are especially important in weakly screened 2D systems.
  • Its property coverage enables benchmarking, structure–property analysis, machine-learning applications, computationally cheaper model parametrization, and modeling of van der Waals heterostructures.Available band structures, spin–orbit splittings, effective masses, and monolayer polarizabilities provide inputs for tight-binding, k · p, and QEH-based models.
  • Combinatorial screening identified potentially synthesisable materials including ferromagnets with large magnetic anisotropy, high-mobility semiconductors, and visible-frequency plasmonic metals.
  • The predictions describe perfect crystalline materials, while future extensions are needed for adsorbates, point defects, additional spectra, and the database’s continuing property expansion.The current database is described as a snapshot, and automated calculation of Raman, infrared, or XPS spectra is not straightforward.
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