Source-linked AI summary
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
TL;DR
Reliable records of computed 2D-material properties depend on data quality and numerical precision. The paper introduces the C2DB, which calculates material properties using DFT and many-body methods, and identifies potentially synthesizable materials with notable magnetic, electronic, and plasmonic properties.
Problem
For computed materials-property records, data quality depends on numerical precision.
Source: §1 · p. 6Method
The C2DB calculates two-dimensional-material properties using DFT and many-body methods.
Source: §2 · p. 9, §4 · p. 70Results
The C2DB identifies potentially synthesizable 2D materials, including ferromagnets with large magnetic anisotropy, semiconductors with high intrinsic carrier mobility, and metals with plasmons in the visible frequency range.
Source: §4 · p. 72Takeaways & Limitations
The open C2DB provides a resource for computational modeling of two-dimensional materials and van der Waals heterostructures.
Source: §4 · pp. 70, 72The methods are generally not quantitatively accurate for excited-state properties such as electronic band structures and optical absorption spectra.
Source: §1 · p. 6
Abstract
from arXiv · showhide
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 introduction presents C2DB as an open, consistent first-principles resource that organizes accessible datasets on 2D materials and reports a stability-screened set of potentially synthesizable monolayers. It outlines examples spanning band energies, excitons, plasmonics, magnetism, and high-mobility semiconductors.
1 Introduction
- The introduction motivates higher-level treatments because standard DFT is generally not quantitatively accurate for excited-state band structures and optical absorption spectra.Computational databases also support open data sharing, benchmarking, and machine-learning analyses of materials correlations.Source: §1 · p. 6
- C2DB organizes ab-initio properties for more than 1500 isolated monolayers generated by combinatorial decoration of known crystal prototypes.Its properties span structural, thermodynamic, magnetic, elastic, electronic, dielectric, and optical data.Source: §1 · p. 7
- All materials use the same code, parameter settings, and workflow, with HSE06 and many-body methods used for accurate electronic and optical properties.The database employs G0W0 for band structures and RPA and the Bethe-Salpeter Equation for optical properties.Source: §1 · p. 7
- The C2DB is freely accessible online and available for direct download.Users can browse it using simple or advanced queries.Source: §1 · p. 7
- Across more than 1900 monolayers distributed over 32 different crystal structures, the study finds 350, with around 200 completely new and potentially synthesisable 2D materials.The synthesisability criteria used 55 materials experimentally synthesised in monolayer form as a guideline.Source: §1 · p. 8
- Using many-body G0W0 calculations as a reference, the authors assess DFT functionals for band gaps, band edges, and heterointerface alignment, then propose a low-cost strategy for accurate band energies.The overview identifies this as an example of how C2DB data can be used to compare methods and develop a practical strategy.Source: §1 · pp. 8–9
- Using 250 BSE calculations, the authors examine exciton binding-energy trends and provide an unbiased assessment of the accuracy and limitations of the Mott-Wannier model for 2D excitons.Source: §1 · p. 9
- The authors present strong empirical evidence against a k · p-derived relation between effective masses and band gaps using data from more than 600 semiconductor monolayers.Source: §1 · p. 9
- The authors propose a 2D-metal plasmon-dispersion model based on intraband plasma frequency and interband-transition onset, and use it to identify metals with optical-frequency plasmons.Source: §1 · p. 9
- The authors propose new magnetic 2D materials, including metals and semiconductors, with ferromagnetic or antiferromagnetic ordering and significant out-of-plane magnetic anisotropy.Source: §1 · p. 9
- The authors identify new high-mobility 2D semiconductors, including some with band gaps suited to optoelectronic applications.Source: §1 · p. 9
2 Workflow · 2.1 Structure relaxation
C2DB generates materials from prototype-based structures, relaxes them across magnetic configurations, and applies stability and geometry screens before calculating properties. Its workflow includes many-body calculations for a restricted subset and checks structural and lattice-constant reliability.
2 Workflow
- The workflow relaxes structures first, then calculates properties with DFT and many-body methods; G0W0 and BSE are limited to semiconductors with at most four unit-cell atoms.Properties are computed only after materials satisfy stability and geometry criteria.Source: §2 · p. 9
- Online database properties include spin-orbit coupling by default, while most properties are also calculated and stored without it.Source: §2 · p. 10
- Calculations use GPAW with plane-wave basis sets and PAW potentials, managed by ASE scripts that the authors made freely available under GPL.Source: §2 · p. 10
2.1 Structure relaxation
- Candidate structures begin with experimentally known crystal prototypes decorated with atoms from a chemically reasonable subset of the periodic table.Materials are named by unit-cell formula followed by the prototype structure.Source: Figure 2 · p. 13, §2.1 · p. 13
- Unit cells and atomic coordinates are relaxed in NM, FM, and AFM configurations, with AFM calculations restricted to cells containing at least two metal atoms.The initial seed-structure symmetries are preserved during relaxation.Source: §2.1 · pp. 13–14
- Most candidates become fully connected 2D structures below a covalent factor of 1.3; around 100 disconnected candidates are excluded.The workflow checks covalent connectivity using covalent radii increased by 30% and advances materials with exactly one 2D cluster.Source: §2.1 · p. 14, Figure 3 · p. 14
- Duplicate structures are screened by same-formula RMSD using a 0.01 Å threshold; metastable FM and AFM ground states are treated separately as phases.Source: §2.1 · pp. 14–15
- Across 29 monolayers, the lattice-constant mean absolute deviation from Ref. 42 was 0.024 Å (0.4%), attributed to differences in PAW potentials.The comparison used VASP with PBE and similar numerical settings.Source: §2.1 · p. 15
2.2 Crystal structure classification · 2.3 Thermodynamic stability
C2DB classifies crystal structures by symmetry and prototype criteria, and assesses thermodynamic stability against competing phases while treating convex-hull predictions as qualified estimates.
2.2.1 Symmetry
- Crystal symmetry is classified by determining the 3D space group with Spglib on the 3D supercell, using a tolerance of 10^-4 Å.Source: §2.2.1 · p. 15
2.2.2 Prototypes
- Materials share a prototype only if they have the same space group and stoichiometry and comparable thicknesses, distinguishing structures with different numbers of atomic layers.The thickness criterion separates, for example, monolayer hBN and GaS.Source: §2.2.2 · p. 15
- Each prototype has a representative material; established conventions are used when available, while novel prototypes are represented by the material lowest in energy relative to the convex hull.Source: §2.2.2 · p. 16
2.3 Thermodynamic stability
- PBE heat-of-formation accuracy is around 0.2 eV/atom on average, while convex-hull energy errors are estimated below 0.1 eV for 35 compounds compared with vdW-compliant exfoliation energies (Ref. 18).C2DB uses pure PBE energies to preserve transparency and reproducibility.Source: §2.3 · pp. 18–19
- A negative heat of formation is necessary but not sufficient for stability: the material must lie below all competing phases on the convex hull, a criterion not directly decisive for 2D stability or synthesisability [47].DFT energy uncertainty, substrate or other external stabilization, and kinetic barriers can make a monolayer metastable despite lower-energy phases.Source: §2.3 · p. 18
- The convex hull comprises 2,836 most stable binary bulk compounds from OQMD.24; their energies were recalculated with GPAW and PBE using the 2D materials’ numerical settings, without re-optimizing structures.Source: §2.3 · p. 19
- Because bulk reference energies may be overestimated by omitted attractive vdW interactions, layered monolayers can appear below the hull even when their bulk phases are more stable.This bias is linked to the different treatment of the OQMD bulk references and the monolayers.Source: §2.3 · p. 19
- Most 2D materials lie above the convex hull and are predicted unstable freestanding, whereas antiferromagnetic FeSe lies slightly below it and is predicted stable, consistent with observed AFM order in monolayer FeSe on SrTiO3 [48].The authors caution that hull predictions are guidelines because PBE formation-energy errors can be sizable.Source: §2.3 · p. 19
2.4 Phonons and dynamic stability
The C2DB tests dynamical stability using Γ-point phonons of a 2 × 2 supercell, which detects some local distortions but is not a full phonon-band test. It combines dynamical and thermodynamic stability ratings to classify materials and guide which continue through the workflow.
2.4 Phonons and dynamic stability
- Γ-point phonons for a 2 × 2 cell are calculated by finite displacements of each primitive-cell atom by ±0.01 Å; negative dynamical-matrix eigenvalues signal instability.The induced forces build the dynamical matrix, whose eigenvalues are the squares of mass-renormalised phonon frequencies.Source: §2.4 · p. 20
- The test checks local distortions with periodicities up to 2 × 2, a necessary but not sufficient stability condition that can flag instabilities at larger periodicities.A 2 × 2-cell dynamical matrix can have negative eigenvalues even when the spontaneous relaxation would produce a larger-period structure.Source: §2.4 · pp. 20–21
- The test can miss imaginary phonons in the Brillouin-zone interior when none occur at the zone boundary; a full phonon band structure would be needed for a rigorous test.The passage notes that such missed modes can produce out-of-plane buckling or charge-density-wave reconstructions with several-unit-cell periodicities.Source: §2.4 · p. 21
- To avoid duplicate entries, the workflow compares RMSD between structures relaxed from T and T′ starting phases, which may relax back to the same structure.Structures below the figure's dashed RMSD line are considered identical.Source: §2.4 · p. 21
2.4.1 Stability criteria
- All but five experimentally known monolayers have hull energy below 0.2 eV/atom, and three of those five were synthesized only on metal substrates.The comparison covers experimentally synthesized or exfoliated monolayers in the C2DB.Source: §2.4.1 · p. 23, Figure 7 · p. 24
- Each material receives separate low, medium, or high dynamical and thermodynamic ratings; its overall rating is the lower one, and low-rated materials do not continue through the workflow.High overall stability denotes materials considered likely stable and potentially synthesisable.Source: §2.4.1 · p. 23
2.5 Elastic constants
This section describes C2DB’s planar elastic-stiffness calculations and reports agreement with prior PBE results, using isotropic-material consistency as a numerical-convergence check.
2.5 Elastic constants
- In two dimensions, stress and strain each have three independent components—planar x and y, plus shear—and the symmetric stiffness map has up to six independent components.Source: §2.5 · p. 25
- For all C2DB materials, C11, C22, and C12 are estimated from central-difference stress derivatives after ionic relaxation under ±1% axial strains, chosen to suppress noise while remaining linear.Strains are applied along the x or y coordinate axis.Source: §2.5 · p. 26
- C2DB planar stiffness coefficients agree very well with published PBE results; isotropic MoS2, WSe2, and WS2 show up to 0.6% variation between C11 and C22, testing numerical convergence.Table 3 presents planar stiffness coefficients in N/m and compares this work with prior calculations.Source: Table 3 · p. 26, §2.5 · p. 26
2.6 Magnetic anisotropy · 2.7 Projected density of states · 2.8 Band structures
This section describes how the C2DB characterizes magnetic anisotropy and orbital-resolved states and computes spin-orbit-coupled band structures using DFT and selected G₀W₀ calculations. It also evaluates the G₀W₀ band-structure workflow through comparisons with prior calculations and experiments, reporting numerical convergence and limitations of the employed potentials.
2.6 Magnetic anisotropy
- Magnetic anisotropy arises from spin-orbit coupling and is evaluated from eigenvalue differences; negative EMA(i) indicates an out-of-plane easy axis.For magnetic materials, EMA(i) is the energy difference between out-of-plane and in-plane magnetisation, for i = x or y.Source: §2.6 · pp. 26–27
2.7 Projected density of states
- The PDOS identifies the atomic orbitals contributing to bands by species and angular-momentum channel, and linear-tetrahedron interpolation returns exactly zero where no states exist.Source: §2.7 · pp. 27–28
2.8 Band structures
- Band structures follow high-symmetry paths for five 2D Bravais lattices, using PBE, HSE06, and GLLBSC, with G0W0 for finite-gap materials having up to four atoms per cell.The G0W0 calculations covered around 250 materials, and SOC was included by non-self-consistent diagonalisation in the full Kohn-Sham eigenstate basis.Source: §2.8 · p. 28
2.8.1 PBE band structure
- 0.041 eV mean absolute deviation was found between C2DB PBE+SOC band gaps and VASP results for 29 monolayers.Source: §2.8.1 · p. 29
2.8.3 GLLBSC fundamental gap
- GLLBSC band energies were up-shifted relative to G0W0, so the database stores only the fundamental gap and Δxc; symmetric correction of PBE band edges is suggested for absolute edges.The gap center is described reasonably well by PBE.Source: §2.8.3 · p. 33
2.8.4 G0W0 band structure
- The G0W0 calculations use truncated Coulomb interactions to avoid unphysical screening from repeated layers, but this slows k-point convergence; an analytical screened-interaction expression addresses the issue.Source: §2.8.4 · pp. 33–34
- The G0W0 self-energy opens the WS2 band gap by 1.00 eV relative to PBE and 0.47 eV relative to HSE.The comparison uses band structures including spin-orbit coupling.Source: §2.8.4 · p. 34
- The workflow reproduces prior G0W0 gaps for 51 monolayer TMDCs with a mean absolute error of around 0.1 eV.The difference is attributed to using PBE rather than LDA as the starting point and to the analytical expression for W around q = 0.Source: §2.8.4 · p. 34
- Published monolayer MoS2 QP band gaps range from 2.40 to 2.90 eV (114–121); comparing prior G0W0 results is not meaningful because implementations and parameter settings differ substantially.Most reported calculations do not employ a truncated Coulomb interaction and thus suffer from spurious screening effects.Source: §2.8.4 · p. 34
- G0W0 band gaps for three monolayer TMDCs and phosphorene are all within 0.2 eV of experiment.The experimental values were corrected for substrate interactions but not zero-point motion, expected to be small (< 0.1 eV).Source: §2.8.4 · p. 35
- The employed PAW potentials are not norm-conserving and can cause errors for bands with highly localized states, mainly 4f and 3d orbitals.Including vertex corrections and using norm-conserving potentials are identified as future C2DB work.Source: §2.8.4 · p. 35
2.9 Band extrema
For finite-gap materials, the workflow identifies the VBM and CBM positions in the Brillouin zone and their energies relative to the vacuum level. It defines that level from the asymptotic electrostatic potential, with a two-sided average for materials with an out-of-plane dipole.
2.9 Band extrema
- For finite-gap materials, the workflow records the VBM and CBM positions in the Brillouin zone and their energies relative to vacuum.The vacuum level is defined by the asymptotic electrostatic potential.Source: §2.9 · p. 35
- The PBE electrostatic potential defines the vacuum level used in non-selfconsistent HSE and G_0W_0 calculations.Source: §2.9 · p. 35
- For materials with an out-of-plane dipole, the workflow applies a dipole correction in selfconsistent DFT and defines vacuum as the average of the asymptotic potentials on both sides.The PBE vacuum-level shift is stored in the database; Figure 12 illustrates the vacuum-level splitting for MoSSe.Source: §2.9 · p. 37, Figure 12 · p. 37
2.10 Fermi surface
The C2DB calculates Fermi surfaces for all metallic compounds using PBE with spin-orbit coupling, then interpolates eigenvalues and plots them in the first Brillouin zone. The section illustrates the method with spin-projected bands for VO2-MoS2.
2.10 Fermi surface
- For every metallic compound, the Fermi surface is calculated with PBE including spin-orbit coupling from a ground-state calculation using a k-point density of at least 20/Å^-1.Eigenvalues are interpolated with quadratic splines and plotted within the first Brillouin zone.Source: §2.10 · pp. 37–38
- The VO2-MoS2 ferromagnetic ground state has a magnetic moment of 0.70 µB per unit cell and alternating spin-polarized lobes with ⟨Sz⟩= ±1.Source: §2.10 · p. 38
- Figure 13 shows the VO2-MoS2 Fermi surface in the MoS2 crystal structure, colored by the out-of-plane spin projection ⟨Sz⟩.The plotted Fermi surface is calculated with PBE and spin-orbit coupling.Source: Figure 13 · p. 38, §2.10 · p. 38
2.11 Effective masses
The C2DB calculates effective masses from PBE band curvatures using third-order polynomial fits, and reports very satisfactory agreement with previously published PBE data. It also calculates exciton reduced masses and illustrates anisotropic, spin-orbit-coupled band structure in SnS.
- For bands within 100 meV of the CBM or VBM, third-order polynomial fits stabilize curvature estimates and make masses less sensitive to k-point grids.Source: §2.11 · pp. 38–39
- The mass tensor is diagonalized to obtain heavy and light masses for anisotropic bands, with masses and band splittings calculated both with and without SOC.Source: §2.11 · p. 39
- The exciton reduced mass is calculated from direct valence-conduction transition energies; its relation to electron and hole masses does not hold for indirect-gap materials.Source: §2.11 · p. 39
- For SnS in the GeSe structure, both bands are anisotropic; SOC splits the valence band by ∼10 meV, while a Rashba effect splits the conduction band.The Rashba effect arises from SOC combined with the perpendicular electric field created by the structure’s permanent dipole.Source: §2.11 · p. 39
- Agreement between selected C2DB and previously published effective masses calculated with PBE and including SOC is described as very satisfactory.Source: §2.11 · pp. 39–40
2.12 Work function · 2.13 Deformation potentials · 2.14 Plasma frequencies
These sections describe how the C2DB calculates work functions for metals, deformation potentials for semiconductors, and plasma frequencies for metals. They also report strain-induced band-gap closing in MoS2 and negligible local-field effects on the intraband response.
2.12 Work function
- For metallic compounds, work function is the difference between the Fermi energy and the asymptotic electrostatic potential in vacuum, calculated for PBE and HSE band structures.Both calculations include spin-orbit coupling and use a uniform k-point grid of density 12.0/Å−1.Source: §2.12 · p. 40
2.13 Deformation potentials
- For semiconductors, deformation potentials quantify band-edge energy shifts under linear lattice deformation and estimate acoustic electron-phonon coupling strength.They are also relevant to strain-engineering band gaps and to estimating band-edge or gap uncertainty from lattice-constant uncertainty.Source: §2.13 · pp. 40–41
- The deformation potentials use a central-difference derivative, with ±1% strain applied separately along x and y while ions relax at fixed unit cell.The change in band energy is measured relative to vacuum; calculations use PBE, and nearly degenerate bands are tracked to avoid confusing crossings.Source: §2.13 · p. 41
- Tensile strain in the x direction shifts both MoS2 band edges down, with a larger conduction-band shift that closes the band gap.Figure 15 compares the band energies under biaxial strain with full DFT results and estimates from deformation potentials evaluated at ±1% strain.Source: §2.13 · pp. 41–42, Figure 15 · p. 42
- C2DB deformation potentials generally agree well with literature values; some discrepancy from Ref. 133 is attributed to including spin-orbit coupling.The comparison is for PBE absolute deformation potentials of the VBM and CBM; no table values are provided in the passages.Source: §2.13 · p. 42, Table 6 · p. 42
2.14 Plasma frequencies
- Local-field effects are negligible for the intraband component of a metal’s 2D polarizability, so it can be evaluated separately as a Fermi-surface integral.The intraband response is treated with a Drude expression in the long-wavelength limit.Source: §2.14 · p. 43
- The C2DB calculates x- and y-polarized 2D plasma frequencies for all metals using tetrahedral interpolation of matrix elements and eigenvalues from PBE band structures including SOC.The calculations use a k-point density of 20/Å; the plasma frequency determines the intraband response and, neglecting interband transitions, the plasmon dispersion.Source: §2.14 · pp. 43–44
2.15 Electronic polarisability
The section defines a natural 2D polarizability from induced dipole moment per area, describes its RPA calculation, and presents representative MoS2 and NbS2 spectra.
Electronic polarisability
- 2D polarizability is defined through induced dipole moment per unit area, integrating the unit-cell-averaged polarization out of plane so α2D = Lα.L is the unit-cell length perpendicular to the slab.Source: §2.15 · p. 44
- For all database materials, the RPA polarisability is calculated for in-plane and out-of-plane polarization in the optical limit; metallic intraband contributions are treated separately.The single-particle eigenvalues and states are calculated using PBE.Source: §2.15 · p. 45
- 1.6 eV is the PBE band gap of MoS2 and the onset of dissipation; its initial Im α is constant, as expected for a 2D material with parabolic dispersion.The static Re α at zero frequency is approximately 6 Å.Source: §2.15 · pp. 45–46
- The RPA in-plane polarisability is also shown for metallic NbS2, with its real part displayed both with and without intraband contributions.Figure 16 compares monolayer MoS2 in the H phase and NbS2 in the T phase.Source: §2.15 · p. 46, Figure 16 · p. 46
2.16 Optical absorbance
The section describes RPA and BSE optical-absorption calculations for selected 2D materials, highlighting excitonic features, agreement with experiment, and sensitivity of exciton binding energies to k-point sampling.
2.16 Optical absorbance
- RPA and BSE absorption spectra were calculated for finite-gap materials with up to four atoms per unit cell, for fields parallel and perpendicular to the layers.The calculations use PBE states with a scissors shift to the G0W0 gap, or the GLLBSC gap for non-magnetic materials and HSE gap for magnetic materials when G0W0 gaps are unavailable.Source: §2.16 · pp. 46–47
- In MoS2, the low-energy in-plane BSE spectrum is dominated by the A and B excitons and agrees excellently with experiment.The two peaks are separated by 0.15 eV, attributed to spin-orbit splitting in the valence band at K.Source: §2.16 · p. 47, Figure 17 · p. 48
- At 48 × 48 k-points, the MoS2 exciton binding energy is 0.53 eV, versus 0.47 eV extrapolated to infinite sampling.The database uses 48 × 48 k-points, and the figure indicates this sampling overestimates the extrapolated binding energy by about 0.06 eV.Source: §2.16 · p. 48, Figure 18 · p. 49
- Exciton binding energies decrease as k-point sampling increases, so C2DB values may be slightly overestimated, while compensating G0W0 gap errors make BSE-G0W0 peak positions converge faster.Electronic excitations converge slowly with k-points because the dielectric function is non-analytic near q = 0.Source: §2.16 · pp. 47–48
- Calculated first-excitonic peak positions agree well with experiment for four transition-metal dichalcogenides and phosphorene; substrate-induced redshifts are expected to be small.Substrate screening reduces exciton binding energies, but also reduces quasiparticle gaps, largely cancelling the change in peak position.Source: §2.16 · p. 48
3 Database overview
This section surveys C2DB materials, their stability, and trends and correlations across electronic, magnetic, and optical properties. Case studies address candidate semiconductors and magnetic and plasmonic materials, as well as the scope and limits of models for predicting exciton binding energies.
3.1 Materials
- The C2DB contains 55 materials shown in Figure 7 plus seven metal-organic perovskites that have been experimentally synthesized in monolayer form.These materials are marked with literature references. Additionally, 80 C2DB monolayers could potentially be exfoliated from experimentally known layered bulk structures; the relevant bulk-compound database IDs are provided.Source: §3.1 · pp. 50–51
- The authors list selected stable materials they report as not previously experimentally known, presenting them as candidates for further study and experimental synthesis.Table 9 gives their magnetic state, formation energy, energy above the convex hull, work function, PBE gap, and whether the gap is direct or indirect.Source: §3.1 · p. 51, Table 9 · p. 53
- 0.12 eV is the mean energy above the convex hull for high-dynamic-stability materials, versus 0.25 eV for other materials; greater dynamic stability tracks with greater thermodynamic stability.The materials naturally form two clusters by dynamic stability.Source: §3.1 · p. 51, Figure 19 · p. 54
3.2 Properties: Example applications
- The case studies examine band gaps and alignment, effective masses and mobility, magnetic order, plasmons, and excitons to explore trends and correlations and showcase C2DB applications.The analysis also reports novel candidate materials for closer future study.Source: §3.2 · p. 55
3.2.1 Band gaps and band alignment
- Relative to G0W0, PBE underestimates band gaps by 45%, HSE06 by more than 20%, while GLLBSC band gaps are only 2% smaller on average.Source: §3.2.1 · pp. 55–56
- Figure 21 marks qualitatively wrong DFT band alignments against G0W0 for heterobilayers; the analysis assumes bands line up with a common vacuum level and neglects interfacial hybridisation and charge transfer.Source: Figure 21 · p. 57, §3.2.1 · p. 57
3.2.2 Effective masses and mobilities
- The mobility analysis considers phonon-limited mobility as intrinsic mobility, absent sample-specific or external scattering sources.The passage notes that measured mobility depends on sample purity, geometry, and, for 2D materials, substrate or embedding-layer interactions.Source: §3.2.2 · p. 58
- Across about 600 semiconductors, electron and hole masses show no clear correlation; mean masses are 0.9 m0 and 1.1 m0, respectively, and 80% versus 65% lie below m0.The data show no clear correlation between effective mass and inverse band gap either; the cross-correlation is below 0.02 for both carrier types, contrary to the expected general k·p linear relation.Source: §3.2.2 · p. 58
- The Takagi estimate links a small deformation-potential–effective-mass product to high mobility, but assumes isolated parabolic bands and a restricted temperature regime for acoustic-phonon scattering.Its temperature conditions require an acoustic-phonon population approximated by the Rayleigh-Jeans law while optical-phonon scattering remains negligible.Source: §3.2.2 · p. 59
- Phosphorene is predicted to have high mobility for both carrier types, while previously unknown, highly stable materials are also identified as high-mobility candidates.The selected materials have “high” overall stability; their transport properties warrant further study.Source: §3.2.2 · p. 60, Table 11 · p. 62
- For MX2 monolayers, calculated room-temperature electron mobilities are 200–400 cm2V−1s−1, within 50% of ab-initio results, and the estimate ranks five of six material pairs correctly.For MoS2, the estimate is 240 cm2V−1s−1 versus 400 cm2V−1s−1 from a full ab-initio calculation.Source: §3.2.2 · p. 60
3.2.3 Magnetic properties
- For CrI3, the magnetic anisotropy is −0.85 meV per Cr atom; although small, anisotropy is crucial for magnetic order at finite temperature.Source: §3.2.3 · p. 62
- Across compositions, magnetic moment is mainly determined by the metal atom, whereas anisotropy depends strongly on the non-metal: halides generally exceed chalcogenides, and iodine stands out for large anisotropy.Source: §3.2.3 · p. 62
- Large anisotropy does not require a heavy spin-carrying metal: several 3d metal iodides show large values, reflecting interplay among spins, orbital hybridisation, and crystal field.Source: §3.2.3 · p. 63
- Semiconductors show magnetic anisotropies comparable to CrI3, metals show higher values, and medium-stability semiconductors reach 2 meV, potentially supporting Curie temperatures similar to or above CrI3.Source: §3.2.3 · p. 63
- Several 2D materials have antiferromagnetic order, but their PBE-described superexchange interactions require careful verification using PBE+U [161].Source: §3.2.3 · pp. 63–64
3.2.4 Plasmons
- Metallic monolayers can support higher-energy plasmons than graphene, potentially extending 2D plasmonics into the optical regime.Source: §3.2.4 · p. 64
- Several 2D metals have plasmon energies around 1 eV at a 50 nm wavelength, significantly exceeding those in highly doped graphene.Figure 25 presents the plasmon comparison.Source: §3.2.4 · p. 66
3.2.5 Excitons
- The Mott-Wannier model correlates with BSE but deviates by 0.28 eV across materials and 0.20 eV for TMDCs, overestimating strongly bound and underestimating weakly bound excitons.Source: §3.2.5 · p. 68
- Exciton-model errors arise for weakly screened, localized excitons and small-gap materials with nonparabolic bands, where excitons extend over more of the Brillouin zone.For weak screening, the model's homogeneous electron and hole distributions can overestimate binding.Source: §3.2.5 · pp. 68–69
- Breakdown of the parabolic-band approximation explains most cases where the model underestimates binding energy; other errors arise from extra-band contributions and unaccounted anisotropic exciton masses.Source: §3.2.5 · p. 69
- The Mott-Wannier model can describe exciton trends qualitatively, but its quantitative accuracy is limited across materials without parameter tuning.For quantitative estimates, α2D should not be less than 2 Å, and the effective-mass approximation should be checked against the band structure.Source: §3.2.5 · p. 69
- Exciton binding energies correlate with band gap less clearly than Ref. 170 reported, and the authors reject the proposed 1/Egap effective-mass explanation.The rejected explanation attributes the trend to the 1/Egap dependence of exciton effective mass.Source: Figure 26 · p. 70, §3.2.5 · p. 70
4 Conclusions and Outlook
The open C2DB provides systematically calculated properties for a large collection of 2D materials and reports promising new candidates. The conclusions highlight its uses and possible extensions to more realistic materials and modeling tasks.
4 Conclusions and Outlook
- More than 1500 materials across 32 crystal structures are included, with structural, elastic, thermodynamic, electronic, magnetic, and optical properties.The database is open, and the paper describes its current state as a snapshot because it is growing continuously.Source: §4 · pp. 70–71
- The workflow uses beyond-DFT methods including GW, RPA, and BSE, which the authors identify as important for quantitatively accurate band gaps and optical spectra.The paper provides relevant calculation parameters and makes the data-generation scripts freely available under a GPL license.Source: §4 · p. 71
- Beyond lookup, C2DB supports benchmarking codes and methods, exploring structure–property relations, and applying machine learning in materials science.Its documented calculations are also intended to support theoretical models of more complex 2D structures.Source: §4 · p. 71
- The combinatorial screening identified potentially synthesisable 2D materials, including ferromagnets with large magnetic anisotropy, high-mobility semiconductors, and metals with visible-range plasmons.These predictions are based on computed properties of perfect crystalline materials.Source: §4 · p. 72
- Extending C2DB to adsorbed species and point defects could enable more realistic magnetic and optoelectronic assessments and support materials discovery for batteries and electrocatalysis.The current predictions are based on perfect crystalline materials.Source: §4 · p. 72
- Existing band structures, spin–orbit splittings, and effective masses can help parameterize less expensive models for devices, magnetic fields, and heterostructures.The authors also propose adding Wannier-related inputs for minimal-basis Hamiltonians and developing exchange-coupling calculations to predict magnetic transitions and critical temperatures.Source: §4 · p. 72
- C2DB monolayer data can help model van der Waals heterostructures, which are difficult to treat with conventional ab-initio methods, and provide polarizabilities for dielectric-screening models.The available polarizabilities are for the long-wavelength limit.Source: §4 · pp. 72–73
- The authors propose supplementing optical absorbance with Raman, infrared-absorption, and XPS spectra to help experimentalists characterize samples.Automating first-principles calculations of these spectra is not straightforward and will require significant work.Source: §4 · p. 73
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