Exciton-activated effective phonon magnetic moment in monolayer ${\mathrm{MoS}}_2$

Optical excitation of chiral phonons plays a vital role in studying the phonon-driven magnetic phenomena in solids. Transition metal dichalcogenides host chiral phonons at high symmetry points of the Brillouin zone, providing an ideal platform to explore the interplay between chiral phonons and valley degree of freedom. Here, we investigate the helicity-resolved magneto-Raman response of monolayer ${\mathrm{MoS}}_2$ and identify a doubly degenerate Brillouin-zone-center chiral phonon mode at $\sim 270{\mathrm{cm}}^{-1}$. Our wavelength- and temperature-dependent measurements show that this chiral phonon is activated through the resonant excitation of $A$ exciton. Under an out-of-plane magnetic field, the chiral phonon exhibits giant Zeeman splitting, which corresponds to an effective magnetic moment of $\sim 2.5{\mu }_B$. Moreover, we carry out theoretical calculations based on the morphic effects in nonmagnetic crystals, which reproduce the linear Zeeman splitting and Raman cross section of the chiral phonon. Our study provides important insights into lifting the chiral phonon degeneracy in an achiral covalent material, paving a route to excite and control chiral phonons.

Figure 1

Helicity selection rule of the doubly degenerate chiral phonon in monolayer ${\mathrm{MoS}}_2$. (a) Calculated phonon dispersion of monolayer ${\mathrm{MoS}}_2$. (b) Schematics of the doubly degenerate BZ center ${\mathrm{E}}^{\prime \prime }$ phonon modes. The superposition of the LO and TO modes gives rise to the left- and right-handed chiral phonon modes (${\mathrm{\Omega }}_{\pm }$). (c) PL spectra acquired in the ${\sigma }^{+}{\sigma }^{-}$ channel at 12 K using 532 nm (2.33 eV) and 633 nm (1.96 eV) excitation, respectively. Helicity selection rule of the Raman modes in the (d) off-resonance and (e) on-resonance condition in the ${\sigma }^{+}{\sigma }^{+}$ (yellow), ${\sigma }^{-}{\sigma }^{-}$ (green), ${\sigma }^{+}{\sigma }^{-}$ (orange), and ${\sigma }^{-}{\sigma }^{+}$ (blue) polarization channels. The gray shaded areas in (c)–(e) highlight the chiral phonon modes. The spectra in the range of 340–440 ${\mathrm{cm}}^{-1}$ in the ${\sigma }^{+}{\sigma }^{+}$ and ${\sigma }^{-}{\sigma }^{-}$ channels are scaled by a factor of 0.1.

Figure 2

Broken frequency and intensity degeneracy of chiral phonon in the magnetic field. (a) Magnetic field-dependent Raman spectra in the ${\sigma }^{+}{\sigma }^{-}$ (orange) and ${\sigma }^{-}{\sigma }^{+}$ (blue) polarization channels at the excitation wavelength of 633 nm at 12 K. The spectra are vertically offset for clarity. The gray dashed lines are the guide to the eye of the phonon Zeeman splitting. (b) Split chiral phonon frequencies as a function of the magnetic field with linear fits. (c) Comparison between the valley Zeeman splitting of the $A$ exciton determined by magneto-PL (gray circles) and the chiral phonon Zeeman splitting determined by Raman (black squares). Inset shows the split ${\sigma }^{+}$ and ${\sigma }^{-}$ PL peaks at 14 T. (d) Integrated intensity (I.I.) of the split chiral phonon as a function of the magnetic field. (e) Helicity polarization ($\rho$) as a function of the magnetic field with the linear fit. The blue and orange shades indicate the dominant Raman signal.

Figure 3

Chiral phonon activated through exciton transition. (a) Temperature-dependent Raman spectra in the ${\sigma }^{+}{\sigma }^{-}$ (orange) and ${\sigma }^{-}{\sigma }^{+}$ (blue) polarization channels at the excitation wavelength of 633 nm. The spectra are vertically offset for clarity. (b) Integrated intensity (I.I.) of the chiral phonon mode as a function of temperature. (c) Heat map of the temperature-dependent PL spectra measured using 532 nm excitation laser. “A” denotes the $A$ exciton emission. The color scale represents the normalized PL intensity. (d) Raman frequency of the ${\mathrm{\Omega }}_{\pm }$ mode and (e) PL peak energy of the $A$ exciton as a function of temperature. The solid black curve in (e) is the fit to Eq. (1). The black dashed lines in panels (b)–(e) mark the temperature of 180 K where both Raman (${\mathrm{\Omega }}_{\pm }$) and PL ($A$ exciton) spectral intensities rapidly grow.

Figure 4

Theoretical calculations of chiral phonon activities in magnetic field. (a) Fitting of the split chiral phonon frequencies to Eq. (3) derived from the morphic effects. (b) Calculated Raman scattering cross section in the ${\sigma }^{+}{\sigma }^{-}$ (orange) and ${\sigma }^{-}{\sigma }^{+}$ (blue) polarization channels at varying magnetic field. (c) Helicity polarization of Raman scattering cross section as a function of magnetic field exacted from (b). The experimental data (solid square) are overlaid for comparison.

Figure 5

(a) Schematic of the in-plane rotation of monolayer ${\mathrm{MoS}}_2$ sample with an azimuthal angle $\varphi$. (b) Raman intensity of the 270 ${\mathrm{cm}}^{-1}$ mode in the XX (red) and XY (blue) channels as a function of $\varphi$ in a polar plot. (c) Raman spectra in the XX and XY channels at selected angles of $\varphi$. The sharp peak at $\sim 250{\mathrm{cm}}^{-1}$ appears only in the XX channel. It is an $A$ phonon mode that is not detectable in the ${\sigma }^{+}{\sigma }^{-}/{\sigma }^{-}{\sigma }^{+}$ channels. The spectra are vertically offset for clarity.