Spontaneous Polarization Suppression of Exciton-Exciton Annihilation in 3R-Stacked MoS$_2$ Bilayers

Abstract

Rapid exciton-exciton annihilation (EEA) in two-dimensional semiconductors limits access to high-density excitonic regimes essential for efficient optoelectronic operation under strong excitation. Here, we show that EEA is suppressed by repulsive dipole-dipole interactions between interlayer excitons polarized by the spontaneous polarization intrinsic to rhombohedral (3R)-stacked MoS$_2$ bilayers. Using ultrafast pump-probe spectroscopy, we measure an EEA rate of $γ_{\rm EEA}=(5.03\pm0.99)\times10^{-3}$ cm$^2$ s$^{-1}$ in 3R bilayers, which is approximately 18.2-fold smaller than that in monolayers and 2.9-fold smaller than that in nonpolar 2H bilayers. Despite the higher exciton diffusivity recently reported for 3R relative to 2H bilayers, the reduced EEA rate in 3R indicates a rate-limited regime governed by the close-encounter annihilation probability rather than diffusion. A rate-limited annihilation model incorporating a dipole-dipole repulsive potential captures the observed ratio $γ_{{\rm EEA},3{\rm R}}/γ_{{\rm EEA},2{\rm H}}\approx0.35$ for an exciton-exciton encounter distance of $\sim$1.3 nm, consistent with the bilayer exciton Bohr radius. These results show that spontaneous polarization in 3R-stacked bilayers suppresses nonlinear excitonic losses and provides a route toward high-density excitonics.

Figures (4)

• Figure 1: Stacking-dependent symmetry and electronic structure of MoS$_2$ bilayers. (a) 2H (AA$'$) stacking with 180$^\circ$ rotation between layers, restoring inversion symmetry and yielding zero out-of-plane polarization ($P = 0$). (b) 3R (AB) stacking with a lateral shift of one-third of the unit cell, breaking inversion symmetry and inducing an out-of-plane polarization ($P \neq 0$; opposite for BA stacking). (c) Schematic band structure of 2H and 3R bilayers.
• Figure 2: Optical identification of stacking configuration in MoS$_2$ bilayers. (a) Low-frequency Raman spectra of monolayer (ML) and bilayer (BL) 2H and 3R MoS$_2$, labeled ML (2H), ML (3R), BL (2H), and BL (3R). Two interlayer vibrational modes are observed in the BL samples: the in-plane shear mode at $\sim$24 cm$^{-1}$ and the out-of-plane breathing mode at $\sim$40 cm$^{-1}$. Insets: Optical microscope images of 2H and 3R samples. The inner white dashed triangle outlines the BL region, while the area up to the outer white dashed boundary corresponds to the ML region. Scale bars: 10 $\mu$m. (b) Corresponding normalized reflectance spectra. Shaded regions indicate the A and B excitonic resonances.
• Figure 3: Ultrafast exciton dynamics of monolayer and bilayer MoS$_2$ at varying pump fluence. (a--c) Transient reflectance maps, $\Delta R/R_0$, as a function of probe wavelength and pump-probe time delay for (a) monolayer, (b) 2H bilayer, and (c) 3R bilayer measured at a pump fluence of 61.6 $\mu$J cm$^{-2}$. The black curve shows the linear reflectance spectrum $R_0$ in Fig. \ref{['fig2']}(b) with arbitrary scaling. The vertical dashed lines indicate the A-exciton resonance. (d--f) Corresponding $\Delta R/R_0$ kinetics extracted at the A-exciton bleach wavelength at different pump fluences, with bi-exponential fits (black curves). (g--i) Corresponding time evolution of $n_0/n(t)-1$. Solid black lines are linear fits in the EEA-dominated regime ($t \gtrsim 3$ ps), with slopes $n_0 \gamma_{\mathrm{EEA}}$. The inset in (i) enlarges the 3R data for clarity.
• Figure 4: Schematic of EEA suppression in 3R MoS$_2$ bilayers. (a) Illustration of dipole-dipole repulsion, where spontaneous polarization promotes layer-polarized, dipolar excitons. (b) Calculated Boltzmann suppression factor, $U = \exp[-V_{\mathrm{dd}}(r)/k_B T]$, as a function of the in-plane exciton-exciton separation $r$. The red dashed line indicates the measured EEA suppression in 3R relative to the nonpolar 2H bilayer and the corresponding separation ($r \approx 1.26$ nm). The black and gray dashed lines mark plausible separations ($r = 1.0$ and 1.5 nm) and their corresponding suppression factors ($U = 0.13$ and 0.53), respectively.