Rhombohedral BN: Structure & Optical Response

• Rhombohedral BN is a layered sp²-bonded boron nitride polytype with ABC stacking that exhibits distinct electronic and optical properties.
• Stacking order and interlayer spacing in rBN critically affect vibrational modes, second-harmonic generation, and defect photophysics.
• Advanced growth techniques like MOVPE and iron-flux methods enable controlled synthesis of rBN for photonics and quantum applications.

Rhombohedral boron nitride (rBN) is a layered $sp^2$-bonded boron nitride polytype built from two-dimensional hexagonal sheets of alternating B and N atoms with an $ABC$ stacking sequence. In this form, strong in-plane $\sigma$-bonding coexists with weaker interlayer $\pi$-type interactions, so stacking order, interlayer separation, and stacking disorder directly affect the unoccupied electronic states, vibrational response, nonlinear optics, and defect photophysics. Across recent work, rBN is treated both as a distinct layered BN polytype that must be discriminated from $h$BN, Bernal BN, twinned rBN, and turbostratic BN, and as a host material whose broken inversion symmetry or reduced local symmetry modifies quantum-defect selection rules and radiative properties (Olovsson et al., 2022, Gale et al., 21 Feb 2025).

1. Structure, stacking, and nomenclature

Layered rBN consists of hexagonal B–N sheets stacked in an $ABC\ldots$ sequence, in contrast to the $AB\ldots$ or $AA^\prime$ descriptions used for $h$BN in different registry conventions. The in-plane bonding is strong and $\sigma$-type, whereas interlayer coupling is weaker and mediated by $ABC$0-type interactions. X-ray diffraction in one XANES study identified a dominant rBN phase with the $ABC$1 reflection corresponding to $ABC$2 Å, implying $ABC$3 Å; in the same work, a twin-rBN model used $ABC$4 Å and $ABC$5 Å, yielding $ABC$6 Å per layer. Independent work on UV photoluminescence in MOVPE-grown material likewise reported that the interlayer spacing in $ABC$7 BN is essentially identical across stackings at $ABC$8 nm, while a recent iron-flux study refined rBN lattice parameters in the hexagonal setting to $ABC$9 Å and $\sigma$0 Å (Olovsson et al., 2022, Iwański et al., 2024, Desrat et al., 21 Sep 2025).

Several closely related layered polytypes recur in the literature. Twinned rBN is obtained by doubling the rBN unit cell along the $\sigma$1-axis and rotating the repeated cell by $\sigma$2, producing an $\sigma$3 stacking with three inequivalent B sites. Turbostratic BN (tBN) is partially disordered layered BN with planes stacked roughly parallel to the normal but with random in-plane translations and, in reality, rotations; in the cited XANES work it was modeled with fixed random translations and an average interlayer spacing $\sigma$4 Å, spanning $\sigma$5–$\sigma$6 Å. Bernal BN (bBN) and $\sigma$7BN also appear as comparison phases in optical and growth studies (Olovsson et al., 2022, Shi et al., 2024, Iwański et al., 2024).

The symmetry assignment of layered rBN is not presented uniformly across papers. One DFPT study reported $\sigma$8-stacked r-BN in space group $\sigma$9 (No. 166) and point group $\pi$0, whereas recent spectroscopy and iron-flux work described rBN as non-centrosymmetric with space group $\pi$1 and point group $\pi$2. Defect studies also emphasized that the local crystal field experienced by $\pi$3 in rBN is reduced to $\pi$4, in contrast to $\pi$5 in $\pi$6BN (Mishra et al., 22 May 2025, Desrat et al., 21 Sep 2025, Estaji et al., 22 Mar 2026).

A separate nomenclature issue concerns dense rhombohedral BN phases. Two crystal-chemistry papers used “rh-BN,” “rh-B$\pi$7N$\pi$8,” “hexagonal B$\pi$9N$h$0,” or “hexagonal h-B$h$1N$h$2” for predicted three-dimensional $h$3 tetrahedral networks derived from 3R graphite-like precursors. Those phases are structurally and physically distinct from the layered $h$4 polytype usually denoted rBN in spectroscopy, growth, and quantum-defect studies (Matar et al., 2021, Matar et al., 2021).

2. Stability, phase competition, and synthesis

High-level total-energy work places layered rBN among the low-energy BN polymorphs that are very close in energy. In the RPA-based treatment of bulk BN polymorphism, r-BN was identified explicitly as $h$5-BN($h$6); at $h$7 K, $h$8-BN is the ground state and lies about $h$9–$ABC\ldots$0 kJ/mol lower in energy than each of the layered polymorphs $ABC\ldots$1-BN($ABC\ldots$2), $ABC\ldots$3-BN, $ABC\ldots$4-BN($ABC\ldots$5), and $ABC\ldots$6-BN($ABC\ldots$7) (r-BN). At finite temperature, $ABC\ldots$8-BN($ABC\ldots$9) becomes thermodynamically most stable over $AB\ldots$0-BN at $AB\ldots$1 K, while $AB\ldots$2-BN, $AB\ldots$3-BN($AB\ldots$4), and $AB\ldots$5-BN($AB\ldots$6) “follow closely” and all fall within about $AB\ldots$7 kJ/mol of $AB\ldots$8-BN($AB\ldots$9) for $AA^\prime$0 K. This indicates that rBN is thermodynamically competitive near ambient temperature, but not uniquely isolated by a wide stability window (Cazorla et al., 2018).

Recent growth studies show that rBN can be realized by several routes. MOVPE on 70 nm AlN templates on 2-inch sapphire produced samples with tunable $AA^\prime$1BN:rBN ratios; longer ramp times to the $AA^\prime$2C FME stage correlated with higher rBN fractions, and TEM classified one sample as rBN-dominant, one as mixed, and one as $AA^\prime$3BN-rich. Chemical vapor deposition on single-crystal Fe–Ni(111) thin films yielded large-area multilayer BN single crystals with unidirectional AB and $AA^\prime$4 stackings; $AA^\prime$5 stacking was effectively excluded by the “first-meet-first-connect” mosaic stitching mechanism of pyramid-shaped domains. At $AA^\prime$6 Fe, unidirectional alignment reached $AA^\prime$7, continuous single-crystal multilayers were $AA^\prime$8 nm thick, residue non-connecting islands were $AA^\prime$9 nm thick, and intact transfer was demonstrated on $h$0-inch SiO$h$1/Si (Iwański et al., 2024, Shi et al., 2024).

An iron-flux method at atmospheric pressure produced predominantly rhombohedral bulk crystallites. In that study, boron powder and iron powder were mixed at a ratio of $h$2 wt% boron in iron, melted, saturated with nitrogen for 24 hours, and slowly cooled from $h$3C or $h$4C. The resulting BN shell comprised many triangular bulk crystallites, with the largest up to $h$5m laterally and $h$6 mm along the growth axis, and powder XRD indicated $h$7 rBN by weight, with no evidence of turbostratic BN (Desrat et al., 21 Sep 2025).

3. Electronic structure and core-level spectroscopy

All $h$8 BN polytypes discussed in the cited work are wide band gap semiconductors or insulators, but the numerical gap depends strongly on methodology. In the XANES-plus-core-hole DFT study, PBE-GGA underestimated absolute gaps relative to experiment, but relative trends across polytypes were retained: tBN models gave $h$9–$\sigma$0 eV with an average near $\sigma$1 eV, the twin-rBN model yielded $\sigma$2 eV, and rBN lay in the same wide-gap region, typically slightly larger than tBN and comparable to $\sigma$3BN within that methodology. A separate PBE+vdW study reported an indirect $\sigma$4–$\sigma$5 gap of $\sigma$6 eV for r-BN, while many-body calculations for defect-hosted rBN used a host gap of $\sigma$7 eV at the $\sigma$8-point. Another experimental/comparative study summarized rBN as possessing a wide bandgap of approximately $\sigma$9 eV (Olovsson et al., 2022, Mishra et al., 22 May 2025, Estaji et al., 22 Mar 2026, Gale et al., 21 Feb 2025).

The core-level spectroscopy of rBN is especially sensitive to stacking. At the $ABC$00-edge, XANES probes $ABC$01-like conduction states under the dipole selection rule $ABC$02, with absorption coefficient

$ABC$03

Experimentally, the B $ABC$04-edge exhibited a sharp $ABC$05 resonance split by $ABC$06 eV into peaks at $ABC$07 eV and $ABC$08 eV, and a broader $ABC$09 “camel-back” doublet at $ABC$10–$ABC$11 eV with $ABC$12 eV splitting. At the N $ABC$13-edge, the $ABC$14 edge peak occurred at $ABC$15 eV and the $ABC$16 peak near $ABC$17 eV, with a shoulder at $ABC$18 eV (Olovsson et al., 2022).

Calculated chemical shifts provide polytype fingerprints. Using rBN as the reference at the higher-energy $ABC$19 position, the B $ABC$20-edge chemical shifts were $ABC$21 eV for $ABC$22BN, $ABC$23 eV for twin-rBN, and $ABC$24 eV for tBN; monolayer BN lay $ABC$25 eV above rBN. Increasing interlayer spacing shifted the B $ABC$26 peak to higher energy, decreasing spacing shifted it lower, and ten tBN model structures showed an absolute B $ABC$27 dispersion of $ABC$28–$ABC$29 eV. The unusually large $ABC$30 eV experimental splitting at the B $ABC$31-edge was therefore interpreted as a superposition of ordered rBN and turbostratic contributions, consistent with XRD evidence for a dominant rBN phase plus a tBN shoulder. This directly links stacking disorder and interlayer $ABC$32-coupling to band-edge shifts (Olovsson et al., 2022).

The computational framework behind those spectra used all-electron DFT within the full-potential APW+lo scheme in WIEN2k with PBE-GGA and a core-hole final-state approximation. Supercells were $ABC$33 in plane; rBN used 3 layers (54 atoms), $ABC$34BN 4 layers (72 atoms), twin-rBN 6 layers (108 atoms), and tBN 7 layers (126 atoms). Lorentzian broadening employed FWHM $ABC$35 eV at the B $ABC$36-edge and $ABC$37 eV at the N $ABC$38-edge, and enlarging the supercell from $ABC$39 to $ABC$40 changed relative $ABC$41 shifts by only $ABC$42 eV (Olovsson et al., 2022).

4. Vibrational, nonlinear, and ultraviolet optical response

A central theme in recent work is that rBN exhibits stacking-dependent optical activity not present in bulk $ABC$43BN. Because $ABC$44 stacking breaks inversion symmetry in several of the cited studies, bulk rBN supports a nonzero $ABC$45, strong second-harmonic generation, and parametric down-conversion, whereas bulk $ABC$46BN with $ABC$47 stacking suppresses second-order processes. In nonlinear-optical notation, the intensity scaling is written $ABC$48, and phase mismatch in bulk phase-matching contexts is $ABC$49. Experimentally, reflected SHG was recorded from exfoliated rBN under $ABC$50 eV ($ABC$51 nm) excitation, and the cited work noted recent reports of stacking-controlled rBN films with SHG conversion efficiencies up to $ABC$52 (Gale et al., 21 Feb 2025).

First-principles vibrational studies likewise identify stacking-specific fingerprints. In one DFPT study, $ABC$53-stacked r-BN with vdW corrections had $ABC$54 Å and $ABC$55 Å, a cohesive energy of $ABC$56 eV per atom, and an indirect $ABC$57–$ABC$58 gap of $ABC$59 eV. The $ABC$60-point optical modes included low-frequency shear modes at $ABC$61 and $ABC$62 cm$ABC$63, breathing modes at $ABC$64 cm$ABC$65, an $ABC$66 mode at $ABC$67 cm$ABC$68, and a very strong co-active $ABC$69 mode at $ABC$70 cm$ABC$71 with IR intensity $ABC$72 and Raman intensity $ABC$73. The same study emphasized that many r-BN modes are labeled both IR- and Raman-active, unlike the largely mutually exclusive selection rules of $ABC$74BN (Mishra et al., 22 May 2025).

An experimental iron-flux study proposed a more restrictive primitive-cell picture for rBN: a rhombohedral primitive cell with two atoms, point group $ABC$75, and only six phonon modes in total. In that description, rBN is characterized spectroscopically by the absence of any low-energy Raman mode near $ABC$76 cm$ABC$77, the presence of an extended Raman band from $ABC$78 cm$ABC$79 to $ABC$80 cm$ABC$81, and an in-plane $ABC$82 mode near $ABC$83 cm$ABC$84 with FWHM $ABC$85 cm$ABC$86. The same work argued that treating $ABC$87 stacking in a non-primitive hexagonal cell can obscure the absence of the shear mode at $ABC$88 by band folding (Desrat et al., 21 Sep 2025).

Ultraviolet defect spectroscopy provides another sensitive discriminator. For the $ABC$89 eV carbon-dimer defect $ABC$90 (CBCN), cryogenic PL and CL established a ZPL at $ABC$91 eV ($ABC$92 nm) for rBN and $ABC$93 eV ($ABC$94 nm) for $ABC$95BN, a shift of $ABC$96 meV. The rBN ZPL was asymmetric and broadened on its low-energy side by coupling to acoustic and low-energy out-of-plane phonons; the hBN ZPL was symmetric with FWHM $ABC$97 meV, whereas the high-energy side of the rBN ZPL fit a Gaussian with FWHM $ABC$98 meV. The Huang–Rhys factor increased from $ABC$99 in $\sigma$00BN to $\sigma$01 in rBN, and low-energy out-of-plane modes near $\sigma$02 meV contributed to the rBN lineshape. Time-resolved PL yielded $\sigma$03 ns for $\sigma$04BN and $\sigma$05–$\sigma$06 ns for rBN-dominated samples (Iwański et al., 2024).

Near the band edge, low-temperature PL of high-quality iron-flux crystals showed that rBN retained the four principal phonon-assisted transitions known from $\sigma$07BN, but all were red-shifted. A linear fit of rBN peak energies against $\sigma$08BN peak energies gave an offset of $\sigma$09 meV, and fitting to the rhombohedral dispersion was consistent with an indirect gap of $\sigma$10 eV for rBN compared with $\sigma$11 eV for $\sigma$12BN. A weak ZA-assisted transition at $\sigma$13 eV was observed in rBN and interpreted as symmetry-allowed in non-centrosymmetric rBN (Desrat et al., 21 Sep 2025).

5. Quantum defects, single-photon emission, and spin physics

rBN has become a distinct quantum-defect host because stacking modifies both optical selection rules and spin relaxation pathways. For the negatively charged boron vacancy $\sigma$14, $\sigma$15BN was described as providing $\sigma$16 symmetry with mirror-parity labels, so the lowest triplet transitions are parity-forbidden and emission is vibronically activated. In rBN, the local crystal field is reduced to $\sigma$17; the mirror parity is removed, and a direct zero-phonon optical transition from the $\sigma$18 ground state to the first $\sigma$19 triplet excited state becomes allowed. Many-body GW+BSE calculations placed the first excitonic peak at $\sigma$20 eV and the room-temperature PL center at $\sigma$21 eV ($\sigma$22 nm). Jahn–Teller $\sigma$23 coupling lowered the excited-state energy by $\sigma$24 eV with JT barriers of $\sigma$25 meV, and the total Huang–Rhys factor was $\sigma$26, implying $\sigma$27 (Estaji et al., 22 Mar 2026).

The radiative-rate estimate for the rBN $\sigma$28 ZPL used

$\sigma$29

with $\sigma$30 and $\sigma$31 D, yielding $\sigma$32s for the $\sigma$33 emission in rBN. In $\sigma$34BN, the corresponding parity-forbidden transition has $\sigma$35s and quantum efficiency $\sigma$36. The predicted brightness enhancement in rBN was at least one order of magnitude, and the many-body analysis indicated up to two orders of magnitude increase in $\sigma$37 (Estaji et al., 22 Mar 2026).

The spin Hamiltonian for $\sigma$38 was written as

$\sigma$39

For rBN, theory gave $\sigma$40 GHz, consistent with experiment near $\sigma$41 GHz in irradiated rBN; the $\sigma$42-tensor was approximately isotropic with $\sigma$43, and three equivalent nearest-neighbor $\sigma$44N nuclei produced a resolved seven-line hyperfine pattern with $\sigma$45 MHz per $\sigma$46N. A separate spin-phonon study found that $\sigma$47 in rBN has a longer room-temperature $\sigma$48 than in $\sigma$49-stacked $\sigma$50BN despite the opening of single-quantum relaxation channels by symmetry reduction. The key out-of-plane mode in rBN appeared at $\sigma$51 meV, slightly above the $\sigma$52 meV mode in $\sigma$53BN, and the spin-phonon coupling amplitude in rBN was about four times weaker than in $\sigma$54BN. Across monolayer BN, $\sigma$55BN, and rBN, the high-temperature regime showed the universal $\sigma$56 scaling characteristic of two-phonon Raman relaxation (Estaji et al., 31 Mar 2025, Estaji et al., 22 Mar 2026).

Deterministic single-photon emitters have also been demonstrated in rBN. Electron irradiation activated blue B-center emitters whose room-temperature ZPL occurred at $\sigma$57 eV in rBN versus $\sigma$58 eV in $\sigma$59BN; at $\sigma$60 K, the rBN B-center ZPL was blue-shifted by $\sigma$61 meV relative to $\sigma$62BN. Autocorrelation measurements gave $\sigma$63 for rBN and $\sigma$64 for $\sigma$65BN. Vibronic replicas at $\sigma$66 meV and $\sigma$67 meV were attributed to TO and LO phonons, a replica near $\sigma$68 meV appeared in both polytypes, and rBN exhibited an additional broad shoulder around $\sigma$69 meV attributed to out-of-plane vibrational modes. Comparative DFT-based vibronic simulations favored an in-plane trans-C$\sigma$70 defect as the most likely microscopic origin of the B-center in both $\sigma$71BN and rBN (Gale et al., 21 Feb 2025).

6. Applications, unresolved issues, and related rhombohedral BN phases

The combination of bulk nonlinear optics, quantum emitters, and spin defects gives rBN a distinct position among van der Waals materials. One recent study explicitly placed rBN alongside SiC as a platform that simultaneously offers intrinsic second-order nonlinearity and quantum defects for integrated photonics, and another argued that the direct $\sigma$72 ZPL transition in rBN, together with $\sigma$73s, $\sigma$74 GHz, and $\sigma$75s, makes room-temperature single-defect ODMR feasible without relying on ensembles or cavities. Suggested application directions include magnetometry, thermometry, strain sensing, frequency conversion, and entangled-photon generation in hybrid van der Waals photonic structures (Gale et al., 21 Feb 2025, Estaji et al., 22 Mar 2026).

Several identification problems remain active. Conventional $\sigma$76 XRD reflections are poor polytype discriminants because interlayer spacings are nearly identical across layered BN stackings, and high-frequency Raman modes are only weakly sensitive to stacking in many geometries. This has motivated the use of B $\sigma$77-edge XANES, SHG, and defect-related UV photoluminescence as stacking-sensitive probes. Even then, overlap with turbostratic disorder or stacking-fault-related bands can complicate interpretation: the XANES study explained a large $\sigma$78 splitting through rBN+tBN superposition, and the UV PL study noted that $\sigma$79 emission in the $\sigma$80–$\sigma$81 eV range overlaps with stacking-fault-related bands, so rBN was established structurally rather than by a uniquely isolated PL line in that energy window (Olovsson et al., 2022, Iwański et al., 2024, Shi et al., 2024).

Methodological limitations are also explicit in the cited work. PBE-GGA underestimates absolute band gaps; GW/BSE corrections are needed for quantitative agreement, especially for excitonic features. Vibrational effects are required to reproduce the $\sigma$82 camel-back splitting in XANES, tBN models with random translations omitted random rotations, and defect studies did not yet provide full charge stability, formation energies, or quantitative intersystem-crossing rates for $\sigma$83 in rBN. In spin-relaxation theory, low-temperature rates remain more uncertain because finite supercells can miss very low-energy phonons and non-phononic channels may dominate (Olovsson et al., 2022, Estaji et al., 31 Mar 2025, Estaji et al., 22 Mar 2026).

Finally, the term “rhombohedral boron nitride” itself requires care. In most recent spectroscopy, growth, and defect papers it denotes the layered $\sigma$84 $\sigma$85-stacked polytype discussed above. By contrast, crystal-chemistry papers have used rh-B$\sigma$86N$\sigma$87, hexagonal B$\sigma$88N$\sigma$89, or rh-BN/h-B$\sigma$90N$\sigma$91 for predicted dense three-dimensional $\sigma$92 rhombohedral networks with lattice parameters such as $\sigma$93 Å and $\sigma$94 Å in one formulation, or $\sigma$95 Å and $\sigma$96 Å in another, bulk moduli of $\sigma$97–$\sigma$98 GPa, and indirect gaps near $\sigma$99 eV. Those predicted ultra-hard phases are chemically stoichiometric BN, but they are not the same material as layered rBN and should not be conflated with the $\pi$00 $\pi$01-stacked host used in XANES, nonlinear-optical, and quantum-defect studies (Matar et al., 2021, Matar et al., 2021).