Near-Surface Divacancy Defects in 2D Materials

Updated 14 November 2025

Near-surface divacancy defects are point defects formed by the removal of two adjacent atoms near a material's surface, altering electronic, spin, and structural features.
In graphene, the (585) defect produces resonant scattering and potential edge-induced magnetism, while in SiC, these defects stabilize quantum emitter behavior.
Optimized surface passivation and precise defect engineering are key to achieving long-term optical stability and enhanced spin coherence in quantum photonic devices.

Near-surface divacancy defects are point defects formed by the removal of two adjacent atoms near a material's surface or interface, resulting in distinctive electronic, spin, and structural properties that are crucial in the context of quantum sensing, spintronics, and nanophotonic technologies. In two-dimensional (2D) materials such as graphene and wide-bandgap semiconductors like silicon carbide (SiC), the atomic coordination and symmetry breaking at or near the surface mediate unique defect reconstructions and lead to pronounced modifications of the defect's optical, electronic, and magnetic characteristics.

1. Atomic Structure and Reconstruction

Graphene

In graphene, the canonical divacancy is the "5–8–5" (or "(585)") defect, created by removing two adjacent carbon atoms (Ugeda et al., 2011). The reconstructed core comprises an octagon flanked by two pentagons, saturating all dangling $\sigma$ -bonds and preserving a planar structure with D $_{2h}$ symmetry. Characteristic bond lengths and bond angles in the defect core differ from pristine values and are summarized below:

Parameter	Pentagon Edge	Octagon Edge	Bulk Graphene
C–C bond length (Å)	1.39	1.46	1.42
Bond angle (degrees)	≈108	≈135	≈120

STM imaging at cryogenic temperatures reveals (585) defects as quasi-elliptical protrusions $\sim$ 0.3 nm in diameter, with electronic density modulations extending $\sim$ 1 nm. The long mirror axis is rotated 30° with respect to the graphene lattice vectors (Ugeda et al., 2011).

Silicon Carbide

In SiC, the neutral divacancy consists of adjacent silicon and carbon vacancies (V $_{\rm Si}$ V $_{\rm C}$ ). Near (H-passivated) surfaces in cubic 3C-SiC, the defect core remains similar to bulk but increasingly distorts with proximity to the surface (Viglione et al., 12 Nov 2025). In nanostructures such as nanowires, the surface morphology and chemistry—especially whether the surface is hydrogenated, hydroxylated, or fluorinated—critically determine the presence or absence of in-gap states and the preservation of the defect's quantum levels (Ngomsi et al., 30 Mar 2024).

2. Energetics and Surface Effects

Formation Energies

The thermodynamic stability of near-surface divacancies is quantified via the formation energy:

$E_{\rm f} = E_{\rm tot}^{\rm def} - E_{\rm tot}^{\rm pristine} + 2\mu_{\rm C},$

where $E_{\rm tot}^{\rm def}$ and $E_{\rm tot}^{\rm pristine}$ are the total energies of the defective and pristine supercells, and $\mu_{\rm C}$ is the chemical potential per atom (for C in graphene $\approx$ –9.20 eV) (Ugeda et al., 2011). For the (585) defect, $E_{\rm f}\approx7.6$ eV in the bulk, reduced ( $\sim$ 7.2 eV) when formed near graphene ribbon edges (Jaskolski et al., 2015).

In SiC, although absolute numbers are not universally quoted, the defect formation energy near a surface is generally lower than deep in the bulk due to strain relaxation and reduced constraint, but becomes sensitive to surface states and passivation chemistry (Ngomsi et al., 30 Mar 2024).

3. Electronic and Spin Structure

Graphene: Non-Magnetic Resonant Scattering

The (585) divacancy in pristine graphene introduces a nearly dispersionless (flat) $\pi$ -band centered at $E_{\rm res} \approx +150$ meV above $E_F$ , yielding a pronounced asymmetric resonance in the density of states (DOS) with width $\Delta E \approx 0.3$ eV (Ugeda et al., 2011). Spin-resolved DFT finds no net magnetization: the state is spin-degenerate with total magnetic moment 0 $\mu_B$ .

Zigzag Graphene Nanoribbons: Edge-Induced Magnetism

When (585) divacancies are positioned within a few lattice constants of a zigzag edge, strong mixing between defect-localized and edge bands occurs (Jaskolski et al., 2015). This hybridization lifts the degeneracy of the edge states, resulting in asymmetric spin splitting and a net ferromagnetic moment localized on the edge-defect subsystem. Quantitative results include spin moments reaching 2 $\mu_B$ per defect (for edge-proximal, dilute limits) and local spin splittings $\Delta E \sim 0.15$ eV within the hybridized bands. The effect vanishes for divacancies situated near the ribbon center.

SiC: Spin-Triplet Multiplet Structure and Zero-Field Splitting

In both 4H and 3C polytypes, the ground state of the neutral divacancy is a spin triplet, well described by the Hamiltonian

$H_e = -\gamma_e\,\mathbf{B}\cdot\mathbf{S} + D(S_z^2 - \tfrac{1}{3}S(S+1)) + E(S_x^2 - S_y^2),$

where $D$ and $E$ are the axial and transverse zero-field splitting (ZFS) parameters (Viglione et al., 12 Nov 2025). Surface proximity induces significant changes:

Depth (nm)	D (MHz, Axial)	E (MHz, Axial)	D (MHz, Basal)	E (MHz, Basal)
0.6	1384	–166	1457	–45
1.2	1401	–30	1466	–63
Bulk	1418	0	1418	0

For axial orientation, $|E|$ decays rapidly with depth; $D$ approaches bulk values for $z\gtrsim1.2$ nm (Viglione et al., 12 Nov 2025). Basal defects retain larger $D$ and persistent $|E|\sim60$ MHz regardless of depth.

4. Optical, Charge-State, and Quantum Coherence Properties

4H-SiC: Stacking-Fault-Protected Near-Surface Divacancies

Divacancy centers fabricated within stacking faults via focused helium ion beam (FHIB) irradiation (30 keV, spot size $\approx$ 0.5 nm, dose 200–400 ions/spot) at $\sim$ 170 nm below the surface exhibit notable charge and spectral stability (He et al., 20 Feb 2024). The stacking-fault quantum well provides band-offset protection, suppressing non-radiative ionization events.

Key properties of stacking-fault divacancies (“PL6” centers):

Observable	Value
Ionization rate	$\Gamma_{\rm PL6}=6.5$ MHz/W × $P_{\rm res}$
PLE linewidth	$E_x: 721\pm28$ MHz; $E_y: 820\pm29$ MHz
Spectral drift	$\Delta\nu\sim50$ MHz over 3 h
Spin coherence	$T_2^*=2.84~\mu$ s; $T_2=55.6~\mu$ s

Compared to carbon-implanted divacancies (FWHM $\sim$ 6–7 GHz, $T_2^*\sim0.45~\mu$ s, $T_2\sim22~\mu$ s), stacking-fault divacancies show a $\sim$ 7-fold linewidth narrowing and 6-fold enhancement of $T_2^*$ (He et al., 20 Feb 2024).

Surface Passivation and State Elimination in SiC

Electronic structure calculations on nanostructured SiC reveal that uniform H or H/OH passivation of the surface removes all in-gap surface states, restores the band gap to near-bulk values (E $_{\rm gap}\approx3.02$ eV), and recovers the defect’s zero-phonon line (ZPL) to within 40 meV of bulk (Ngomsi et al., 30 Mar 2024). Fluorination leaves residual valence-band-edge resonances and is unsuitable for quantum emitter stabilization. The passivation route stabilizes charge and spin states and preserves narrow optical emission relevant for high-fidelity quantum photonic operations. This suggests that similar passivation is essential for maintaining stable, near-surface divacancy qubits in real SiC nanodevices.

5. Experimental Probes and Measurement Techniques

Scanning Probe and Spectroscopic Characterization

STM/STS at cryogenic temperatures ( $\sim$ 6 K) resolves the local atomic and electronic signatures of graphene divacancies at the surface, directly linking real-space structure to electronic resonance features at $E_{\rm res} \approx +150$ meV (Ugeda et al., 2011). In SiC, photoluminescence excitation (PLE) spectroscopy combined with advanced ion-beam writing allows deterministic placement and high-resolution measurement of single near-surface divacancy centers (He et al., 20 Feb 2024).

Angle-resolved PLE reveals C $_{3v}$ symmetry–split optical dipoles with mutually orthogonal polarizations. Hahn-echo and Ramsey pulse sequences quantify spin coherence and provide room-temperature $T_2$ values. Ionization rates are inferred from time-resolved fluorescence decay upon resonant optical driving.

Spin Hamiltonian and Open-System Simulation

Spin resonance and dynamical control in SiC are modeled using the full triplet Hamiltonian with hyperfine, dipolar, and driven-dissipative terms. Simulations (e.g., using QuTiP) show that achievable Rabi π/2 pulses are of order 1 μs for drive frequencies $\Omega_R = 0.2$ –0.3 MHz, suitable for quantum control cycles prior to dominant decoherence for near-surface defects (Viglione et al., 12 Nov 2025).

6. Roles in Quantum Technologies & Materials Science

Near-surface divacancy defects serve as tunable nodes for electron transport, magnetism, quantum sensing, and photonic interfacing:

Graphene: (585) divacancies act as efficient resonant scatterers, modulating conductivity and carrier mean free path. Edge-proximal (585) divacancies in zigzag nanoribbons induce localized ferromagnetic order, enabling the engineering of edge-magnetization via controlled vacancy placement (Jaskolski et al., 2015).
SiC Quantum Devices: Stacking-fault-protected, near-surface divacancies exhibit long-term charge stability, sub-GHz optical linewidths, and multi- $\mu$ s spin coherence. These features are essential for high-fidelity spin-photon entanglement, quantum networking (e.g., at 1038 nm), and integration into photonic nanostructures (He et al., 20 Feb 2024). Depth-dependent control over zero-field splitting and local strain coupling permits the design of tailored qubit arrays and sensors with nm-scale spatial addressing capability (Viglione et al., 12 Nov 2025).

A plausible implication is that further integration of deterministic fabrication (FHIB), quantum-well engineering, and surface chemistry optimization will be required to maximize performance and scalability in near-surface quantum technologies.

7. Surface Chemistry, Passivation, and Defect Engineering Strategies

Surface termination chemistry exerts a decisive influence on the electronic, optical, and charge-state stability of near-surface divacancy defects.

Hydrogen and Mixed H/OH Passivation: These treatments completely eliminate in-gap surface states, restore bulk-like electronic gaps (SiC: Eg $\approx$ 3.0 eV), and stabilize the defect’s ZPL and charge state (Ngomsi et al., 30 Mar 2024). For defects $<2$ nm from the surface, such passivation is required to avoid blinking, bleaching, or spectral wandering deleterious to quantum operation.
Fluorination: Results in incomplete passivation; the strong ionic character of Si–F and C–F bonds reintroduces surface resonances and destabilizes the defect charge configuration under photoexcitation.
Mechanical Design: Strain at the defect site contributes only minor shifts ( $\sim$ 2 meV) to the ZPL, compared to stochastic surface chemistry effects. Thus, electronic and chemical environment control is dominant.

Design guidelines for robust near-surface divacancy quantum devices include: (i) axial orientation placement at depths $\gtrsim$ 1 nm below a hydrogenated surface; (ii) engineering of stacking faults or quantum wells to favor charge-state robustness; and (iii) exclusion of surface treatments that introduce partially filled or resonant levels within the bandgap.

Near-surface divacancy defects, through their distinctive atomic reconstructions and surface-sensitive quantum properties, represent critical building blocks for low-dimensional physics and quantum technologies. Their electronic, spin, and optical characteristics can be selectively engineered via surface chemistry, structural orientation, and proximity effects, with immediate implications for the rational design of quantum sensors, spintronic devices, and integrated photonics platforms.