Breaking of Valley Degeneracy by Magnetic Field in Monolayer ${\mathrm{MoSe}}_2$

Using polarization-resolved photoluminescence spectroscopy, we investigate the breaking of valley degeneracy by an out-of-plane magnetic field in back-gated monolayer ${\mathrm{MoSe}}_2$ devices. We observe a linear splitting of $-0.22\mathrm{meV}/\mathrm{T}$ between luminescence peak energies in ${\sigma }_{+}$ and ${\sigma }_{-}$ emission for both neutral and charged excitons. The optical selection rules of monolayer ${\mathrm{MoSe}}_2$ couple the photon handedness to the exciton valley degree of freedom; so this splitting demonstrates valley degeneracy breaking. In addition, we find that the luminescence handedness can be controlled with a magnetic field to a degree that depends on the back-gate voltage. An applied magnetic field, therefore, provides effective strategies for control over the valley degree of freedom.

Figure 1

(a) Experimental geometry showing back-gated monolayer ${\mathrm{MoSe}}_2$ devices in out-of-plane magnetic fields. Luminescence is excited with light from a 1.89 eV laser diode and collected separately for ${\sigma }_{+}$ and ${\sigma }_{-}$ polarization in the Faraday geometry. (b) Schematic of the fiber-coupled optical cryostat used in the experiment. (c) Optical micrographs of devices $D1$ and $D2$. (d) Luminescence spectra of $D2$ taken at 0 T and 4.2 K with $-30$, 0, 10, and 50 V back-gate voltage.

Figure 2

(a) Polarization-resolved luminescence spectra from monolayer ${\mathrm{MoSe}}_2$ ($D1$) at 4.2 K for ${\sigma }_{+}$ and ${\sigma }_{-}$ detection, as excited using unpolarized light at 1.89 eV. From top to bottom, the panels show spectra taken with 0, 6.7, and $-6.7\mathrm{T}$ out-of-plane magnetic fields. Both the polarization and splitting change sign upon reversing the field. (b) Schematic band structure of ${\mathrm{MoSe}}_2$ near the $K_{+}$ and $K_{-}$ points in the absence of a magnetic field, showing the optical selection rules for the $A$ exciton transition studied in this experiment. Within each valley, spin degeneracy is broken at $B=0$ due to spin-orbit coupling [9, 10, 13, 40, 41]. The arrows denote spin angular momentum up and down for the occupied states.

Figure 3

(a) Difference of peak energies found for ${\sigma }_{+}$ and ${\sigma }_{-}$ detection plotted versus the magnetic field for $D1$. Both the exciton (blue triangles) and trion (red circles) show splitting of $-0.22\pm 0.01\mathrm{meV}/\mathrm{T}$ found via a linear fit. The fits are plotted as blue solid and red dashed lines for the exciton and trion, respectively. (b) The schematic band structure of ${\mathrm{MoSe}}_2$ in a magnetic field showing the Zeeman energy $E_Z^{c(v)}$ for the conduction (valence) band. The exciton Zeeman splitting is $2(E_Z^c-E_Z^v)$.

Figure 4

(a) Polarization-resolved luminescence spectra from $D2$ at 4.2 K and 6.7 T for ${\sigma }_{+}$ and ${\sigma }_{-}$ detection, excited with ${\sigma }_{-}$ light at 1.89 eV. From top to bottom, the panels show spectra taken with $-20$ and 51 V gate voltage applied to the substrate. (b) Trion valley splitting versus the magnetic field for selected gate voltages, showing a decrease in slope with gate voltage. (c) Circular polarization of the trion peak $(I_{+}-I_{-})/(I_{+}+I_{-})$ versus gate voltage at 6.7 T (red circles), showing an increase to over 50% as gate voltage is increased. For comparison, we also plot the trion fraction $I_{\text{trion}}/(I_{\text{trion}}+I_{\text{exciton}})$ (black triangles).