Quantum Point Defects in 2D Materials - The QPOD Database

The study addresses how intrinsic point defects (vacancies and antisites) in monolayer 2D semiconductors and insulators influence structural, electronic, magnetic, and optical properties, and how such defects can be harnessed for technologies (spintronics, quantum computing, quantum photonics) versus when they degrade performance. The purpose is to create a high-throughput, reproducible DFT-based workflow and a curated database (QPOD) that systematically characterizes defects across many 2D hosts, providing formation energies, charge transition levels, defect concentrations, Fermi-level pinning, symmetry, transition dipoles, hyperfine coupling, zero-field splitting, and selected excited-state properties. This responds to the need for scalable, benchmarked defect calculations in 2D materials where electrostatics and supercell effects are challenging, enabling screening for defect tolerance, intrinsic dopability, and candidates for quantum applications.

The paper situates the work in the broader context of defect physics and 2D materials: defects play dual roles, degrading transport yet enabling functionalities in spintronics and quantum technologies. Experimental observations include single-photon emission and ODMR in 2D materials (e.g., hBN, MoS2, WSe2). First-principles DFT has become integral to interpreting defect experiments, but high-throughput studies are hampered by supercell size, magnetism, and charged-defect corrections. Workflow systems (ASR, FireWorks, AiiDA) and defect toolkits (pycdt, pydef, ADAQ) exist, yet a comprehensive high-throughput 2D defect database was missing. For charged defects in 2D, long-range electrostatics complicate corrections; Slater–Janak transition-state approaches have been used for CTLs in various materials and can circumvent electrostatic correction issues. Advanced methods (hybrid functionals, GW) offer higher accuracy but are too costly for large-scale studies; PBE generally yields reliable thermodynamics though with band-gap underestimation and delocalization errors.

• Host selection and supercells: Starting from C2DB, non-magnetic, thermodynamically (Ehull < 0.2 eV/atom and |ΔHhost| < 0.2 eV/atom) and dynamically stable monolayers with PBE band gap > 1 eV were filtered. From 281 candidates, 82 hosts were selected using a supercell density criterion (Ne × Vsupercell < 0.9 Å^3) plus handpicked known 2D materials (MoS2, hBN, WS2, MoSe2); for polymorphs, the lowest ΔHhost was retained. Supercells were built via integer combinations of primitive vectors, with constraints to break symmetry, ensure >15 Å minimum defect–defect distance, minimize atom count, and optimize homogeneity.
• Defect generation: For each inequivalent Wyckoff site, intrinsic defects include all vacancies and antisites (substitutions by other host species). Example: MoS2 yields VS, VMo, MoS, and SMo.
• Formation energies and concentrations: Defect formation energy for defect X and charge q is Ef[X] = Etot[X] − Etot[bulk] − Σi ni μi + q EF, with μi set to elemental standard states; vibrational/entropic terms neglected. Equilibrium concentration Ceq[X] = NX gX exp(−Ef/kBT). Charge neutrality Σq q [CXq] = n0 − p0 yields a self-consistent Fermi level EF at given T, with carrier densities from DOS and Fermi–Dirac distribution referenced to the VBM.
• Charge transition levels via Slater–Janak (SJ): CTLs ε(q/q±1) obtained by integrating KS eigenvalues over fractional occupations, assuming linearity, avoiding charged-supercell electrostatic corrections. Reorganization energies λq computed as total-energy differences between equal-charge states at different geometries; KS eigenvalues referenced using averaged electrostatic potential at a remote equivalent atom (or vacuum, giving similar results).
• Symmetry analysis: Defect point group G determined by mapping the relaxed defect into a symmetry-preserving supercell (for spglib). In-gap states are projected onto irreducible representations via character analysis using truncated integrals within a cutoff radius (~2 Å) around the defect center to exclude low-symmetry supercell tails.
• Optical matrix elements and radiative rates: Transition dipole moments between localized in-gap KS states computed in real space (μ = ⟨ψn|r|ψm⟩). Spin-conserving radiative rates follow standard dipole emission formula using EZPL (including reorganization energy). Excited-state geometry optimization for accurate lifetimes performed only for selected systems.
• Hyperfine coupling (HF): Hyperfine tensor AN includes Fermi-contact (trace/3) and dipolar anisotropic parts, derived from spin density at/near nuclei using PAW formalism; principal values tabulated for all atoms in the supercell.
• Zero-field splitting (ZFS): For S = 1 states, D tensor obtained from spin–spin dipolar interaction; axial (D = 3Dzz/2) and rhombic (E = (Dxx − Dyy)/2) parameters characterize splitting of ms sublevels.
• Excited states (DO-MOM): Excited electronic states computed via direct optimization of orbital rotations combined with maximum overlap method to stabilize non-Aufbau solutions, including open-shell singlets via linear combination approach (Es = 2Est − Et − Ed). Photoluminescence (PL) lineshapes from generating-function method using partial Huang–Rhys factors Sk derived from mass-weighted displacements and ground-state phonon modes.
• Workflow and data: Automated via ASR with MyQueue. Ground-state workflow: relax neutral defect, compute density, identify in-gap states, SJ with half-integer occupations; if in-gap states relative to EF exist, perform charged relaxations up to ±3. Data extraction: Ef, CTLs (with/without relaxation), equilibrium EF and defect/carrier concentrations, symmetry labels, HF, ZFS, transition dipoles, metadata. Excited-state workflow applied to selected high-spin defects with KS gaps ≥ 0.5 eV and limited SOC; PL lineshapes and ZPL/hyperparameters computed for a final subset.
• DFT settings: GPAW (plane-wave), 800 eV cutoff; k-point density 6 Å^-1 for relaxations, 12 Å^-1 for ground states; PBE functional; fixed supercells, atomic forces < 0.01 eV/Å; Fermi smearing 0.02 eV (0.2 eV for relaxations, increased up to 0.1 eV if needed); Pulay mixing with separate total and magnetization densities. Excited states at Γ, same parameters; DO-MOM with maximum step length pmax = 0.2. SJ calculations use ground-state parameters. Benchmarking performed on a subset prior to production.

• Database scope: >1900 defect systems covering various charge states of 503 intrinsic point defects (vacancies and antisites) across 82 2D semiconductors/insulators; web-app interlinked with C2DB.
• Formation energies: Neutral defects show similar distributions for vacancies and antisites with means near 4 eV. 44% have Ef < 3 eV and 28% have Ef < 2 eV, indicating many defects can form readily during growth. Defect Ef correlates with host heat of formation ΔHhost (more stable hosts resist defect formation) and with host band gap (larger gaps correlate with more negative ΔHhost and higher Ef).
• Structural relaxation: Relaxations significantly affect defect energetics, especially for antisites; reorganization energies for CTLs can exceed 2 eV and are crucial for accurate CTLs and charged Ef. Charged-state relaxations started from neutral geometries reduce additional reorganization.
• Charge transition levels (CTLs): CTLs generally lie within the pristine band gap or near band edges, supporting sufficient supercell sizes. Including relaxation lowers EA and raises −IP (i.e., ε(0/+1) increases, ε(0/−1) decreases). In rare cases (e.g., VFe in ZrF2), ordering −IP < EA is inverted, implying neutral-state instability.
• Intrinsic dopability and carrier concentrations: Self-consistent Fermi levels at 300 K show most hosts are intrinsic or n-type; no hosts exhibit intrinsic p-type behavior. Example: Janus AsClSe has an electron concentration of 9.5 × 10^13 cm−2 at 300 K (n-type). Many materials have low intrinsic carrier concentrations, indicating good external dopability. The study of 58 hosts was used for intrinsic carrier-type analysis (with degeneracies set to 1).
• Defect tolerance (optical): Vacancy CTLs tend to be shallower than antisites: 55% of vacancies vs 30% of antisites produce shallow states (CTLs within 0.1Eg of band edges). Thus vacancies are, on average, less detrimental to optical properties than antisites. Identification of defect-tolerant ionic insulators is reported.
• Symmetry of relaxed defects: 34% C1 (no symmetry), 20% Cs (single mirror). 31% fall into C2, C3v, or C4v; C4v defects (≈20%) are common in hexagonal hosts (e.g., VS, WS in WS2; VSe in SnSe; CaBr in CaBr2) and share the symmetry of the NV center. About 10% change point group upon charging.
• High-spin and quantum candidates: ~80 defects exhibit high-spin (S > 1/2) ground states; 80 triplets initially considered, 33 with KS gaps ≥ 0.5 eV; after excluding heavy-element systems, 25 underwent excited-state calculations. Four with small ΔQ were analyzed for PL lineshapes: VSi, CH, SiH in SiCH2 (C3v symmetry). Calculated radiative lifetimes: 1.3 × 10^3 ns (VSi, majority spin HOMO→LUMO), 4.9 × 10^−2 ns (SiH, minority spin), 2.9 × 10^−4 ns (SiH, singlet), 9.0 × 10^−4 ns (CH, majority spin). Extremely small Huang–Rhys factors for Ci-like center indicate narrow PL, rare in 2D. SiH in SiCH2 shows level structure and HR factor reminiscent of NV−, suggesting a potential 2D analogue.
• Additional dopability findings: Several semiconductors (e.g., MgS2H2 and Janus AgClS, AgClSe) exhibit high intrinsic electron concentrations, while intrinsic p-type behavior is absent.

The comprehensive DFT workflow and SJ-based CTL methodology enable consistent, high-throughput characterization of intrinsic defects in 2D materials. The results demonstrate that many defects have modest formation energies, implying their relevance in realistic samples. The correlation between host stability/band gap and defect formation propensity provides guidance for choosing materials for either low-defect optoelectronic applications (favoring large gap, stable hosts) or for color-center-based quantum technologies (large-gap hosts but with specific defect types). Intrinsic Fermi-level analysis shows prevalent intrinsic or n-type behavior and underscores the scarcity of intrinsic p-type 2D semiconductors, mirroring bulk trends; nevertheless, generally low carrier concentrations indicate good external dopability. Vacancy defects are statistically less harmful to optical performance than antisites due to more frequent shallow CTLs, supporting defect-engineering strategies that avoid mid-gap antisites. The symmetry analysis highlights a significant fraction of C4v-like centers analogous to NV, which, combined with triplet-ground-state filtering and excited-state analysis, yields a short list of promising candidates. Among these, selected defects in SiCH2 show narrow PL and favorable level structures, indicating viable paths to ODMR-active, optically addressable spins in 2D. Overall, the QPOD database offers both a reference for interpreting experiments and a platform for defect discovery and screening.

This work introduces QPOD, the first high-throughput database of intrinsic point defects in 2D semiconductors/insulators, generated via an automated ASR/MyQueue workflow. For 82 hosts and >1900 defect systems, the study provides formation energies, CTLs (SJ-based with relaxation), equilibrium Fermi levels and concentrations, symmetry labels, transition dipoles, hyperfine tensors, ZFS parameters, and selected excited-state/PL data. Key insights include: (i) many defects have low to moderate formation energies; (ii) vacancy defects are generally less optically detrimental than antisites; (iii) intrinsic n-type or intrinsic behavior dominates, with no intrinsic p-type hosts; (iv) a limited subset of defects exhibit high-spin ground states and a smaller set shows narrow PL favorable for quantum applications. Future directions include adopting advanced exchange–correlation approximations (e.g., screened hybrids, GW) for improved accuracy and statistical benchmarking against PBE, expanding the host/materials set, automating excited-state workflows for broad coverage, and exploring more complex defects (divacancies, defect pairs) to discover robust spin centers.

• Exchange–correlation functional: All calculations use PBE, which underestimates band gaps and can suffer from delocalization errors; high-lying defect states above the PBE gap may be missed or mispositioned.
• Charged-defect treatment: Electrostatic corrections are circumvented via Slater–Janak; while validated in various cases, residual approximations remain (e.g., linearity assumption, referencing).
• Defect scope: Only intrinsic vacancies and antisites are included; more complex defects (divacancies, pairs) are not yet covered, potentially omitting key spin centers.
• Materials scope: 82 hosts selected from C2DB; broader chemical/structural coverage could change statistical trends.
• Excited-state sampling: Excited-state calculations were performed manually for a filtered subset (primarily triplets with sufficient KS gaps and limited SOC), limiting generality of PL and lifetime statistics.
• Thermodynamic conditions: Chemical potentials fixed to elemental standard states in reported Ef; growth-condition-dependent μ ranges are not fully explored in the main dataset (i-rich/poor available on the web app).