Valley Splitting and Polarization by the Zeeman Effect in Monolayer ${\mathrm{MoSe}}_2$

We have measured circularly polarized photoluminescence in monolayer ${\mathrm{MoSe}}_2$ under perpendicular magnetic fields up to 10 T. At low doping densities, the neutral and charged excitons shift linearly with field strength at a rate of $\mp 0.12\mathrm{meV}/\mathrm{T}$ for emission arising, respectively, from the $K$ and $K^{\prime }$ valleys. The opposite sign for emission from different valleys demonstrates lifting of the valley degeneracy. The magnitude of the Zeeman shift agrees with predicted magnetic moments for carriers in the conduction and valence bands. The relative intensity of neutral and charged exciton emission is modified by the magnetic field, reflecting the creation of field-induced valley polarization. At high doping levels, the Zeeman shift of the charged exciton increases to $\mp 0.18\mathrm{meV}/\mathrm{T}$. This enhancement is attributed to many-body effects on the binding energy of the charged excitons.

Figure 1

(a) and (b) False color representation of the ${\sigma }_{+}$ and ${\sigma }_{-}$ polarized PL spectra of monolayer ${\mathrm{MoSe}}_2$ in the low-doping regime as a function of the strength of the applied perpendicular magnetic field. The spectra for fields of $\pm 10\mathrm{T}$ are presented below the color map. The spectra are normalized to yield the same integrated intensity for the neutral and charged excitons, with a smooth background subtracted. (c) and (d) Extracted Zeeman shift of the neutral and trion energies for ${\sigma }_{+}$ and ${\sigma }_{-}$ PL. The solid lines are linear fits to the experimental data.

Figure 2

Schematic of valley splitting and polarization from the Zeeman effect and the initial and final states of the neutral and charged exciton emission process. In the presence of an out-of-plane magnetic field, the conduction and valence bands shift according to their respective magnetic moments. The dashed lines denote the bands at $B=0$ and the solid lines correspond to the bands for $B>0$. (a) and (b) The initial and final states of the neutral exciton emission process in the low-doping regime. (c) and (d) The initial and final states of the charged exciton emission process in the low-doping regime. (e) and (f) The initial and final states of the trion emission process in the high-doping regime.

Figure 3

Photoluminescence of monolayer ${\mathrm{MoSe}}_2$ in the high-doping regime as a function of applied magnetic field. All information is as in Fig. 1, except only the negative trion feature is observable, and no data are available for the neutral exciton.