Towards ab initio identification of paramagnetic substitutional carbon defects in hexagonal boron nitride acting as quantum bits

Paramagnetic substitutional carbon (${\mathrm{C}}_{\text{B}},{\mathrm{C}}_{\text{N}}$) defects in hexagonal boron nitride are discussed as candidates for quantum bits. Their identification and suitability are approached by means of photoluminescence (PL), charge transitions, electron paramagnetic resonance, and optically detected magnetic resonance (ODMR) spectra. Several clear trends in these are revealed by means of an efficient plane wave periodic supercell ab initio density functional theory approach. In particular, this yields insight into the role of the separation between ${\mathrm{C}}_{\text{B}}$ and ${\mathrm{C}}_{\text{N}}$. In most of the cases, the charge transition between the neutral and a singly charged ground state of a defect is predicted to be experimentally accessible, since the charge transition level position lies within the band gap. A posteriori charge corrections are also discussed. A near-identification of an experimentally isolated single spin center as the neutral ${\mathrm{C}}_{\text{B}}$ point defect was found via comparison of results to recently observed PL and ODMR spectra.

Figure 1

Substitutional carbon defects in hBN (part 1, neutral paramagnetic, from left to right): ${\mathrm{C}}_{\text{B}},{\mathrm{C}}_{\text{N}}$ (B in ochre, N in cyan, C in purple).

Figure 2

Substitutional carbon defects in hBN (part 2, singly charged paramagnetic, from left to right): ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$-DAP-1 (dimer), ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$-DAP-2, ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$-DAP-$\sqrt{7}$ (B in ochre, N in cyan, C in purple; cf. text for DAPs).

Figure 3

Substitutional carbon defects in hBN (part 4, neutral paramagnetic, from left to right): ${\mathrm{C}}_{\text{2}}{\mathrm{C}}_{\text{B}}$-trimer, ${\mathrm{C}}_{\text{2}}{\mathrm{C}}_{\text{N}}$-trimer (B in ochre, N in cyan, C in purple).

Figure 4

Substitutional carbon defects in hBN (part 3, singly charged paramagnetic, from left to right): ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$-DAP-$\sqrt{13}, {\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$-DAP-4 (B in ochre, N in cyan, C in purple; cf. text for DAPs).

Figure 5

Calculated Kohn-Sham defect levels for neutral carbon defects in the fundamental band gap of hBN. DAP refers to the ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$-DAP donor-acceptor pair defects. The spin-polarized calculation introduces a gap between the occupied (filled triangle) and unoccupied (empty triangle) defect levels for the same orbitals in the different spin channels for half-integer spin defects.

Figure 6

Calculated photoluminescence (PL) spectrum for the neutral point defects (${\mathrm{C}}_{\text{B}}$ and ${\mathrm{C}}_{\text{N}}$, cf. Fig. 1) and basic trimers (${\mathrm{C}}_2{\mathrm{C}}_{\text{B}}$ and ${\mathrm{C}}_2{\mathrm{C}}_{\text{N}}$, cf. Fig. 3) in bulk hBN.

Figure 7

Calculated photoluminescence (PL) spectrum for the five closest neutral DAPs (cf. Figs. 2 and 4) in bulk hBN.

Figure 8

Calculated photoluminescence (PL) spectrum for the five closest singly positive DAPs (cf. Figs. 2 and 4) in bulk hBN.

Figure 9

Calculated photoluminescence (PL) spectrum for the five closest singly negative DAPs (cf. Figs. 2 and 4) in bulk hBN.

Figure 10

Comparing calculated phonon sidebands (PSBs) of candidates (cf. Figs. 1, 2, 3) for identification of optical emitter ${\mathrm{D}}_1$ experimentally isolated by Chejanovsky et al. [12] in hBN.

Figure 11

Charge transition levels (CTLs) of substitutional carbon defects in bulk hBN relative to the valence-band maximum (VBM) obtained directly from screened hybrid DFT [light green (point defects) and dark green (complexes)] and with a posteriori charge corrections [light blue (point defects) and dark blue (complexes)] [40, 41] (cf. the text and Table 3).

Figure 12

Measured ODMR spectrum of isolated optical emitter ${\mathrm{D}}_1$ [12] compared to line broadening calculated for the defect identification candidates ${\mathrm{C}}_{\text{B}}$(0), ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$-DAP-2($+$), ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}-\mathrm{DAP}-4(-), {\mathrm{C}}_2{\mathrm{C}}_{\text{N}}$(0) in bulk hBN, all at an external magnetic field of 42 G, theoretical spectra shifted to match the experimental peak position (cf. the text).

Figure 13

Influence of the nuclear quadrupole interaction (NQI) on the theoretical cw EPR/ODMR spectrum of the neutral point defects in bulk hBN at an external magnetic field of 42 G. (a)/(c) ${\mathrm{C}}_{\text{B}}/{\mathrm{C}}_{\text{N}}$ without NQI, (b)/(d) ${\mathrm{C}}_{\text{B}}/{\mathrm{C}}_{\text{N}}$ with NQI, for first neighbors (see the text for explanation; cf. Table 9).