Giant shift upon strain on the fluorescence spectrum of VN NB color centers in *h*-BN

The work addresses why single-photon emitters (SPEs) in hexagonal boron nitride (h-BN) exhibit widely scattered zero-phonon-line (ZPL) energies and varying magnetic behavior. Given that many emitters occur at edges and wrinkles of h-BN flakes, the authors hypothesize that local strain significantly perturbs defect energy levels and thus their optical emission. They focus on the nitrogen antisite-vacancy pair (V_N N_B) defect, a proposed visible emitter and potential qubit in 2D materials, to determine how strain influences its ZPL and to establish the role of electron-phonon coupling in activating and modulating its optical transitions. This understanding is important for interpreting disparate experimental observations and for enabling strain-engineered quantum photonic devices in 2D materials.

Studies have observed robust room-temperature SPEs in h-BN across a broad visible range, often at flake edges and wrinkles, indicating potential strain effects. Competing defect models exist for visible emitters, and reports suggested two classes of emitters with similar lifetimes, with ZPL scatter attributed to external perturbations such as strain. Other experiments categorized multiple emitter types via cathodoluminescence and photoluminescence, finding stress that did not change brightness and only ~10 meV ZPL shifts, while yet other studies reported small stress-induced shifts, leading to seemingly contradictory results. Theoretical works identified color centers (local defects) as likely sources of SPEs and proposed V_N N_B among candidates with ZPL around 1.9 eV. Prior strain studies often monitored Kohn-Sham level shifts rather than direct ZPL energies. Recent low-temperature measurements decomposed some spectra into pairs of emitters with ZPLs separated by ~15 nm and large overall wavelength variation (600–720 nm), tentatively linked to local strain. Correlated microscopy has measured up to ±2% in-plane strain in h-BN flakes and found pairs of emitters (e.g., 630 and 705 nm) likely connected by strain.

The authors combine group theory with ab initio Kohn-Sham density functional theory (DFT) calculations to quantify strain-ZPL coupling for the V_N N_B defect. Group-theory analysis: They consider the defect’s symmetry, initially C2v before relaxation, introducing defect levels a1, b2, and b1 in the band gap and yielding a 2B2 ground state. Strong coupling to out-of-plane (membrane) B2 phonon modes lowers the ground-state symmetry to Cs (pseudo Jahn-Teller, PJT), while the excited 2A1 state remains at C2v. Within C2v, the axial-strain-induced ZPL shift is expressed as δ = [ε^(22) Δ_B2 − (ε^(11)/2) Δ_A1], where ε^(ij) are strain tensor components and Δ_i are state-specific energy shifts. Mixing between a1 and b2 via B2 strain in Cs is argued to have negligible impact on the linear ZPL shift under basal uniaxial strain, justifying use of the C2v-derived expression. DFT computations: The ZPL is computed as the total energy difference between the excited state and ground state at their respective relaxed geometries (global minima). Strain is modeled by changing supercell lattice constants to apply uniaxial strain either parallel (axial, || C2) or perpendicular (⊥) to the C2 axis. The defect’s electronic levels’ responses to strain are tracked for both ground (Cs) and excited (C2v) configurations. Electron-phonon coupling and PJT analysis: The adiabatic potential energy surface (APES) of the 2B2 ground state is obtained using hybrid HSE DFT. The APES is fit to a PJT model ε±(Q) = ½ M ω^2 Q^2 ± sqrt(Δ^2 + F^2 Q^2), extracting the effective phonon energy ħω and coupling strength F, and the Jahn-Teller stabilization energy. A quantum mechanical solution of the PJT system yields the tunneling (jumping) rate between symmetry-broken minima. Extension to multilayers/bulk: Bulk h-BN is modeled including interlayer van der Waals interaction to assess the persistence of membrane phonon effects and strain-ZPL coupling; differences in ZPL and strain response relative to monolayer are reported.

• The calculated unstrained ZPL for the V_N N_B defect (B2(Cs) ↔ A1(C2v) transition) is 1.90 eV, close to observed emissions near 1.95 eV.
• ZPL shifts quasi-linearly with uniaxial strain in the range −1% to +2%, with a giant coupling magnitude of ~12 eV per unit strain for both parallel (axial) and perpendicular directions.
• ±1% strain leads to ~100 nm variation in emission wavelength. Tensile axial (parallel to C2) strain induces a blueshift; tensile perpendicular strain induces a redshift.
• Strain-induced level shifts explain the ZPL behavior: under tensile axial strain, a1 in the ground state shifts down while occupied b2 shifts up (net blueshift). Under tensile perpendicular strain, a1 shifts up steeply and occupied b2 shifts up moderately, bringing levels closer (net redshift).
• Strong coupling to out-of-plane membrane phonons (B2 symmetry) drives a static pseudo Jahn-Teller distortion: the ground state lowers to Cs while the excited state remains C2v, activating an otherwise weak optical transition.
• PJT parameters from HSE DFT/APES fit: electron-phonon coupling F = 178 meV, phonon energy ħω = 23 meV, Jahn-Teller energy ≈ 95 meV. The ground-state tunneling rate between minima is ~8.4 kHz, indicating a static PJT regime. The coupling is ~2.5× stronger than in the NV center in diamond.
• In bulk h-BN (with interlayer van der Waals interaction), PJT persists with reduced Jahn-Teller energy (50.5 meV) and strong coupling (F = 193 meV). ZPL energies and strain-induced ZPL shifts differ by <0.01 eV from the monolayer case.
• The giant strain response provides a consistent explanation for the wide experimental scatter of visible ZPL wavelengths (e.g., 600–720 nm) in h-BN SPEs, compatible with local strains up to about ±2%. Orientation-dependent blue/red shifts (armchair vs zigzag) align with experimental observations of linear ZPL–strain dependence.

The results show that local strain in h-BN can strongly and linearly modulate the ZPL of the V_N N_B color center due to giant electron-phonon coupling with out-of-plane membrane modes, thereby explaining the wide variability of observed visible emitters’ ZPLs. The PJT-induced symmetry lowering in the ground state activates the dipole-allowed transition, resolving the apparent discrepancy between weak dipole selection rules in high symmetry and the observed brightness. Direction-dependent shifts (blueshift for axial tensile, redshift for perpendicular tensile) and the existence of three possible defect orientations rationalize prior reports of both small and larger shifts under applied stress, and linear ZPL–strain trends. The persistence of strong coupling and similar strain sensitivity from monolayer to bulk indicates that membrane phonon physics remains relevant even in multilayers. These insights have implications for controlling emitter spectra via strain engineering, interpreting spectral broadening and intensity variations, and integrating h-BN emitters into quantum nanophotonic and spin-mechanical platforms where strain can be a control knob.

This study combines group theory and advanced DFT to demonstrate that the V_N N_B defect in h-BN exhibits strong electron-phonon coupling to membrane modes, leading to a static PJT ground state that activates its optical transition and produces a giant, quasi-linear ZPL shift (~12 eV per unit strain). The predicted ~100 nm wavelength modulation at ±1% strain provides a plausible, quantitative explanation for the broad distribution of visible SPE ZPLs in h-BN and their strain dependence. The findings suggest routes to strain-engineer emitter properties, enable nanoscale stress sensing, and support spin-mechanical control schemes in 2D materials. Future work should pursue unambiguous experimental identification of the emitting defects, explore other h-BN defects with similar strain sensitivities, and develop device-level strategies to harness or stabilize strain for reproducible quantum photonic performance.

• The group-theory expression for ZPL–strain response uses C2v symmetry and approximations for the Cs ground state; exact orientation-dependent coupling magnitudes require numerical DFT and are not determined purely by symmetry.
• Linear ZPL–strain behavior is established within a limited strain range (approximately −1% to +2%).
• While monolayer results are extended to bulk including van der Waals interactions, full details of multilayer environments and substrates are not exhaustively treated.
• Unambiguous experimental identification of the specific defect responsible for each observed SPE remains outstanding; the proposed mechanism is consistent but not definitively proven for all emitters.