Carbon trimer as a 2 eV single-photon emitter candidate in hexagonal boron nitride: A first-principles study

The generation of single-photon emitters in hexagonal boron nitride around 2 eV emission is experimentally well recognized; however, the atomic nature of these emitters is unknown. In this Letter, we use first-principles calculations to demonstrate that carbon trimer substitutional defect (${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{N}}$) is a possible source of 2 eV single-photon emitter in hBN. We showcase the calculations of a complete set of static and dynamical properties related to quantum defects, including exciton-defect couplings and electron-phonon interactions, from both density functional theory and many-body perturbation theory. In particular, we show that it is critical to consider both radiative and nonradiative processes when comparing with experimental lifetime for known 2 eV emitters. We find that ${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{N}}$ has several key physical properties matching the ones of experimentally observed single-photon emitters. These include the zero-phonon line (2.13 eV), Huang-Rhys factor (1.35), photoluminescence lifetime (2.19 ns), phonon-sideband energy (180 meV), and photoluminescence spectrum. The identification of defect candidates for 2 eV emission paves the way for controllable single-photon emission generation.

Figure 1

Charged defect formation energy of defects ${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{N}}$ and ${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{B}}$ as a function of Fermi level at (a) N-poor and (b) N-rich conditions.

Figure 2

(a) Single-particle diagram of the ground state ${}_0{}^2\mathrm{A}_2$ at the level of ${\text{G}}_0{\text{W}}_0$@PBE, and (b) ${\text{G}}_0{\text{W}}_0-\text{BSE}$@PBE of ${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{N}}$. VBM and CBM are $-7.431$ and $-0.400\mathrm{eV}$, respectively [70]. The defect states in the band gap are denoted by the irreducible representations of the $C_{2v}$ symmetry group based on the corresponding wave-function symmetry. The isosurface of the wave functions (PBE) is $3\%$ of the maximum. In the ${\text{G}}_0{\text{W}}_0-\text{BSE}$@PBE spectra, the absorption peaks are labeled by the corresponding intradefect transitions. $x$ and $y$ are the in-plane directions that are perpendicular and parallel to the $C_2$ axis, respectively, and $z$ is the out-of-plane direction. The spectral broadening is 0.02 eV.

Figure 3

Multiplet structure and important physical parameters of ${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{N}}$ in hBN. ${}_0{}^2\mathrm{A}_2$ is the ground state, and ${}_1{}^2\mathrm{B}_1$ and ${}_2{}^2\mathrm{A}_2$ are the excited states. The red solid lines denote radiative recombination and the blue dashed lines denote nonradiative recombination. $S$ is the HR factor with full-phonon calculations. ${\tau }^{\mathrm{R}}$ and ${\tau }^{\mathrm{NR}}$ are the radiative lifetime and nonradiative lifetime, respectively. $\eta$ and ${\tau }^{\mathrm{PL}}$ are the QY and PL lifetime, respectively.

Figure 4

Spectral function that shows the distribution of phonon modes and the contribution of phonon modes to the electron-phonon interaction of the ${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{N}}$ defect in hBN. The left vertical axis and black solid line are for the spectral function, and the right vertical axis and red dots are for the partial HR factor as a function of phonon energy. The inset figures are the low-energy phonon mode (60 meV) and dominant phonon mode (187 meV) of ${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{N}}$ for transition ${}_2{}^2\mathrm{A}_2\to {}_0{}^2\mathrm{A}_2$. The red arrows show the atom displacement of the corresponding phonon modes.

Figure 5

The calculated properties of ${\mathrm{C}}_2{\mathrm{C}}_{\mathrm{N}}$ along with the experimental values which are summarized in Table. 1. (a) PL lifetime vs ZPL; (b) HR factor vs ZPL; (c) PSE vs ZPL; (d) comparison between the theoretical PL spectrum (this work) and the experimental PL spectrum (Expt) [13]. In (a), (b), and (c), the blue dots are for the experimental values of $\sim 2\mathrm{eV}$ single-photon emitters, the green dot is for the experimental PL lifetime of $\sim 20\mathrm{ns}$, and the red dots are for the calculated values. The calculated ZPL here is from the ${\text{G}}_0{\text{W}}_0-\text{BSE}$@PBE calculation. The comparison shows that ZPL, PL lifetime, HR factor, and PSE are all in the experimental range. The calculated PL spectrum also matches well with the experimental PL of the $\sim 2\mathrm{eV}$ single-photon emission [13].