Spin splitting in a ${\mathrm{MoS}}_2$ monolayer induced by exciton interaction

By pumping nonresonantly a ${\mathrm{MoS}}_2$ monolayer at 13 K under a circularly polarized continuous wave (CW) laser, we observe exciton energy redshifts that break the degeneracy between B excitons with opposite spin. The energy splitting increases monotonically with the laser power reaching as much as 18 meV, and it diminishes with the increase of temperature. The phenomenon can be explained theoretically by considering simultaneously the band-gap renormalization that gives rise to the redshift and exciton-exciton Coulomb exchange interaction that is responsible for the spin-dependent splitting. Our results offer a simple scheme to control the valley degree of freedom for ${\mathrm{MoS}}_2$ monolayers and provide an accessible method in investigating the many-body exciton-exciton interaction in such materials.

Figure 1

Optical characterization of the sample. (a) The optical image and the AFM mapping of the ${\mathrm{MoS}}_2$ ML, where the inset shows the thickness of the sample is about $0.7$ nm. (b) PL spectrum of the ${\mathrm{MoS}}_2$ ML excited by a 532-nm laser at room temperature. (c) Raman spectrum of the sample at room temperature.

Figure 2

The spectrum of the ${\mathrm{MoS}}_2$ monolayer as a function of the pumping power. (a),(c),(e) Optical spectrum of the sample pumped by a linearly polarized, right-handed circularly polarized, and left-handed circularly polarized laser, respectively, with density of $0.016\mathrm{MW}/{\mathrm{cm}}^2$ and $0.192\mathrm{MW}/{\mathrm{cm}}^2$. The experimental data is shown by circles, the fitting cures are shown using lines. (b),(d),(f) PL peaks (fitted B exciton energy) against the pumping power density (bottom axis), with polarization matching the corresponding spectra on the left columns. Red (blue) dots correspond to B excitons at the $K$ and $K^{\prime }$ valley, respectively. Solid curves are the theoretical plots against $n_c$ (top axis) according to Eq. (4). Theory parameters can be found in Ref. [39].

Figure 3

PL spectra of the ${\mathrm{MoS}}_2$ ML at different temperatures. (a),(c) Optical spectra at 15 and 300 K pumped by a right- and left-handed circularly polarized laser, respectively. The experimental data is shown by circles, the fitting curves are shown using lines. Power density: $0.048\mathrm{MW}/{\mathrm{cm}}^2$. (b),(d) Exciton energy against temperature.