Giant Paramagnetism-Induced Valley Polarization of Electrons in Charge-Tunable Monolayer ${\mathrm{MoSe}}_2$

For applications exploiting the valley pseudospin degree of freedom in transition metal dichalcogenide monolayers, efficient preparation of electrons or holes in a single valley is essential. Here, we show that a magnetic field of 7 T leads to a near-complete valley polarization of electrons in a ${\mathrm{MoSe}}_2$ monolayer with a density $1.6\times 10^{12}{\mathrm{cm}}^{-2}$; in the absence of exchange interactions favoring single-valley occupancy, a similar degree of valley polarization would have required a pseudospin $g$ factor of 38. To investigate the magnetic response, we use polarization resolved photoluminescence as well as resonant reflection measurements. In the latter, we observe gate voltage dependent transfer of oscillator strength from the exciton to the attractive Fermi polaron: stark differences in the spectrum of the two light helicities provide a confirmation of valley polarization. Our findings suggest an interaction induced giant paramagnetic response of ${\mathrm{MoSe}}_2$, which paves the way for valleytronics applications.

Figure 1

A gate controlled ${\mathrm{MoSe}}_2/h\text{−}\mathrm{BN}$ heterostructure under external magnetic field. (a), The sample consists of a $9\mu \mathrm{m}$ by $4\mu \mathrm{m}$ ${\mathrm{MoSe}}_2$ monolayer sandwiched between two $h\text{−}\mathrm{BN}$ layers. Gate voltage applied between the gold contacts to the ${\mathrm{MoSe}}_2$ layer and the highly doped Si substrate allows for controlling the electron density in the monolayer. (b) The single particle picture of conduction and valence band shifts under a magnetic field $B_z$ applied perpendicular to the plane of ${\mathrm{MoSe}}_2$. Assuming a large spin-orbit splitting, only the lowest (highest) energy conduction (valence) band is depicted. For $B_z>0$, the exciton resonance in the $K$ valley redshifts along with the conduction band minimum in the $-K$ valley. This opposite sign of the effective $g$ factor of the excitons and electrons plays a key role in determining the absorption spectrum of ${\mathrm{MoSe}}_2$ monolayers.

Figure 2

Gate voltage dependent photoluminescence spectrum under a magnetic field of $B_z=7\mathrm{T}$. (a) Gate voltage ($V_g$) dependent right-hand circularly polarized (${\sigma }^{+}$) photoluminescence (PL) spectrum of a ${\mathrm{MoSe}}_2/h$-BN heterostructure at $B_z=7\mathrm{T}$ under excitation by a linearly polarized 719 nm laser. The depicted $V_g$ axis is shifted by 10 V to compensate for the hysteretic behavior we observe in the gate scans (see Supplemental Material [26]). (b) The corresponding PL spectrum for left-hand circularly polarized (${\sigma }^{-}$). (c) The line cut through the ${\sigma }^{+}$ and ${\sigma }^{-}$ PL spectra at $V_g=117\mathrm{V}>V_{\mathrm{on},-K}$ show that the PL exhibits a sizable degree of polarization where the ratio of ${\sigma }^{+}$ and ${\sigma }^{-}$ polarized PL intensities is $\simeq 11$. (d) The line cut through the ${\sigma }^{+}$ and ${\sigma }^{-}$ PL spectra at $V_g=79\mathrm{V}$ shows that the degree of PL polarization increases dramatically to yield a ratio of ${\sigma }^{+}$ and ${\sigma }^{-}$ polarized PL intensities $\simeq 700$. (e) The line cut through the ${\sigma }^{+}$ and ${\sigma }^{-}$ PL spectra at $V_g=-15\mathrm{V}$ where both valleys have high $n_e$. The ratio of the right- (${\sigma }^{+}$) and left- (${\sigma }^{-}$) hand circularly polarized PL intensities is reduced back to $\simeq 11$.

Figure 3

Polarization resolved reflection spectrum under a magnetic field of $B_z=7\mathrm{T}$. (a) Gate voltage ($V_g$) dependent right-hand circularly polarized (${\sigma }^{+}$) white light reflection spectrum of the ${\mathrm{MoSe}}_2/h$-BN heterostructure at a magnetic field of $B_z=7\mathrm{T}$. For $V_g\le V_{\mathrm{on},-K}=100\mathrm{V}$ (yellow dashed horizontal line), we observe a blueshift of the exciton resonance whereas the strength of the attractive polaron resonance increases as it redshifts. (b) Reflection spectrum as in (a) but now for left-hand circularly polarized (${\sigma }^{-}$) light. Only for $V_g\le V_{\mathrm{on},K}=70\mathrm{V}$, oscillator strength transfer to the attractive polaron is observed. Whereas the exciton oscillator strengths of the ${\sigma }^{+}$ and ${\sigma }^{-}$ transitions for $V_g>V_{\mathrm{on},-K}$ are nearly identical, the ${\sigma }^{+}$ attractive polaron is much stronger than its ${\sigma }^{-}$ counterpart for $V_{\mathrm{on},K}<V_g<V_{\mathrm{on},-K}$. (c) The differential reflection spectrum of both ${\sigma }^{+}$ and ${\sigma }^{-}$ light at $V_g=127\mathrm{V}$: the two resonances have nearly identical shape and strength but their energies differ by 1.8 meV, yielding a $g$ factor of 4.4. (d) The differential reflection spectrum as in (c) but now at $V_g=69\mathrm{V}$: the splitting between the attractive polaron resonances is 7.3 meV, which corresponds to a $g$ factor of $\simeq 18$. The ${\sigma }^{+}$ exciton or repulsive polaron energy on the other hand is lower than that of ${\sigma }^{-}$ by $\simeq 2.9\mathrm{meV}$, yielding a $g$ factor of $-7.2$. These results demonstrate that exciton-electron interactions strongly modify the magneto-optical response of ${\mathrm{MoSe}}_2$ monolayers. (e) The differential reflection as well as PL spectrum of both ${\sigma }^{+}$ and ${\sigma }^{-}$ light at $V_g=-13\mathrm{V}$.