Zero-phonon line emission of single photon emitters in helium-ion treated MoS$_2$

TL;DR

This work probes the zero-phonon line (ZPL) emission of single-photon emitters in helium-ion treated MoS2, interpreted as sulfur-site vacancies, by combining photoluminescence spectroscopy, first-order coherence, and ab initio GW-BSE calculations. Using the independent boson model (IBM), the authors bound the ZPL linewidth and phonon contributions, finding an upper bound around $110\,\mu\mathrm{eV}$ at $T<20$ K and a lower bound near $30$–$60\,\mu\mathrm{eV}$ at $T<2$ K, with Debye–Waller factors up to ~40%. The first-order coherence measurements yield a coherence time on the order of a few picoseconds, consistent with the ZPL bounds, while GW-BSE calculations predict radiative lifetimes of tens of picoseconds near the ZPL energy ($E \approx 1.75$ eV), aligning with observed spectral features. Time-resolved measurements reveal multi-exponential decay components and long apparent lifetimes (ns), attributed to relaxation and phonon scattering pathways; these results provide microscopic insight into the emission processes of MoS2 SPEs and support their potential integration into quantum photonic platforms.

Abstract

We explore the zero-phonon line of single photon emitters in helium-ion treated monolayer MoS$_2$, which are currently understood in terms of single sulfur-site vacancies. By comparing the linewidths of the zero-phonon line as extracted directly from optical spectra with values inferred from the first-order autocorrelation function of the photoluminescence, we quantify bounds of the homogeneous broadening and of phonon-assisted contributions. The results are discussed in terms of both the independent boson model and ab-initio results as computed from GW and Bethe-Salpeter equation approximations.

Figures (5)

• Figure 1: Defect PL emission and second-order autocorrelation measurement.(a) Photoluminescence spectra of a single-photon emitter (SPE) in helium-ion treated monolayer MoS2 at $T_\text{bath}$$=1.7\K$ (blue) and 15 (purple). The data normalized to the maximum for $T_\text{bath}$$=15\K$. Experimental parameters are $P_\text{exc}$$=500n\W$, $E_\text{exc}$$=1.94\eV$. The data (gray) are fitted by an independent boson model (solid lines) accounting for coupling of the emitter to acoustic phonons. Inset: sketch of the hBN/MoS2/hBN sample structure with a sulfur-site defect highlighted by a red dashed circle. (b) and (c): Measured second-order autocorrelation function $g^{(2)}(\tau)$ (gray dots) of the defect emission with corresponding fits (solid lines) for $T_\text{bath}$$=1.7\K$ (b) and $15\K$ (c)
• Figure 2: Temperature and excitation power dependence of SPE-related photoluminescence.(a) Sketch of the IBM highlighting the contribution from the ZPL (yellow) and a lower tail related to emission of acoustic phonons. (b) Normalized PL spectra for $T_\text{bath}$ ranging from $1.7\K$ (blue) to $T_\text{bath}$$=50\K$ (yellow) with $E_\text{exc}$$=1.94\eV$ and $P_\text{exc}$$=500n\W$. Arrow on top highlights the red-shift of the maximum for an increasing $T_\text{bath}$. (c) Extracted Debye-Waller factor (black dots, DWF) and Huang-Rhys factor (gray dots, HRF) vs. $T_\text{bath}$ for $P_\text{exc}$$=1µ\W$. Dashed lines are guides to the eye. (d) ZPL broadening (yellow dots) vs. $T_\text{bath}$. The open square represents data from a second sample with $T_\text{bath}$ below $200m \K$. Dashed lines highlight the different slopes below and above 20. Yellow area highlights the data spread at low temperature for this cool-down. (e) Excitation power dependence of the extracted Debye-Waller (black) and Huang-Rhys (gray) factor for $T_\text{bath}$$=1.7\K$. (f) ZPL broadening vs. excitation power ($P_\text{exc}$). Yellow area highlights the data spread for low laser powers during this second cool-down. Dashed line highlights a linear trend.
• Figure 3: First-order auto-correlation measurement of the SPE.$g^{(1)}$ of the SPE as a function of the path difference $\Delta s$ (bottom) of the utilized interferometer and correspondingly, the time delay $\Delta \tau$ (top) of the interfering signals. Data are fitted by the sum of a Lorentzian and two exponential tails (dashed lines). Experimental parameters are $T_\text{bath}$$=1.7\K$ , $E_\text{exc}$$=1.94\eV$ and $P_\text{exc}$$=250n\W$.
• Figure 4: Time-resolved photoluminescence of the SPE.(a) Data are measured at $T_\text{bath}$$=1.7\K$ and displayed in gray with exponential fits in blue, purple, and orange. Black line at bottom panel is sum of blue, purple, and orange. Black dotted line is a polynomial fit (cf. Supporting Information). $P_\text{exc}$ as indicated. (b) Power dependence of the extracted decay times $\tau_1$, $\tau_2$, and $\tau_3$. Colors as in (a). (c) Temperature dependence of the extracted decay times at $E_\text{exc}$$=1.94\eV$ with dashed lines as guides to the eye. The extracted decay time at high $T_\text{bath}$ is baptized $\tau^*_1$.
• Figure 5: Ab initio results of radiative decay times for a sulfur vacancy in MoS2. The black line displays the GW-BSE computed absorption spectrum as a function of energy, while the calculated radiative decay times for different exciton states in MoS2 are displayed by dots, with corresponding oscillator strength indicated by the dot size. The colored dots around 1.75 highlight the energy comparable to the photon emission of the SPE as in the rest of the manuscript.