Six-Body and Eight-Body Exciton States in Monolayer ${\mathrm{WSe}}_2$

In the archetypal monolayer semiconductor ${\mathrm{WSe}}_2$, the distinct ordering of spin-polarized valleys (low-energy pockets) in the conduction band allows for studies of not only simple neutral excitons and charged excitons (i.e., trions), but also more complex many-body states that are predicted at higher electron densities. We discuss magneto-optical measurements of electron-rich ${\mathrm{WSe}}_2$ monolayers and interpret the spectral lines that emerge at high electron doping as optical transitions of six-body exciton states (“hexcitons”) and eight-body exciton states (“oxcitons”). These many-body states emerge when a photoexcited electron-hole pair interacts simultaneously with multiple Fermi seas, each having distinguishable spin and valley quantum numbers. In addition, we explain the relations between dark trions and satellite optical transitions of hexcitons in the photoluminescence spectrum.

Figure 1

(a) Helicity-resolved optical transitions in $\mathrm{ML}\text{−}{\mathrm{WSe}}_2$. Light excitation with ${\sigma }_{+}$ (${\sigma }_{-}$) helicity corresponds to optical transitions at the $K$ ($-K$) valley. Resident electrons occupy the bottommost valleys, whereas photoexcited electrons belong in the top valleys. (b) Optical reflectance spectra at 4 K as a function of gate voltage and photon energy. (c), (d) Helicity-resolved magneto-optical reflectance spectra when the out-of-plane magnetic field is 20 T, shown in the spectral and voltage windows that are marked by the dotted box in (b).

Figure 2

(a) Magneto-optical absorption spectra as a function of magnetic field and photon energy in a second device. The voltage level is at the threshold of filling the top CB valley of $K$. The shaded boxes show the regimes at which the top valley at $K$ is filled. (b) Spin- and valley-resolved LL diagrams in the CBs within a single-electron picture. The solid black line denotes the chemical potential of the Fermi sea. (c) The oxciton state, formed when the trion at its core binds to three Fermi holes in the CB and two satellite electrons. The hexciton-to-oxciton transition takes place when the top CB valley at $K$ has one filled Landau level, marked by the shaded regions in (a).

Figure 3

(a) Calculated interparticle distances in the hexciton as a function of the Fermi energy ($E_F\approx 5\mathrm{meV}$ amounts to $n={10}^{12}{\mathrm{cm}}^{-2}$). (a) Results are shown for average distances between the CB electron and VB hole ($r_{he}$), between the two CB electrons of the core trion ($r_{ee}$), between the VB hole and the outer top-valley electron ($r_{ht}$) or CB holes ($r_{h\overline{e}}$), and between the CB holes ($r_{\overline{e}\overline{e}}$). Inset: calculated binding energy of the satellite electron to the hexciton. (b), (c) Schemes of the hexciton in $k$ space and real space, respectively. The trion at the core of the hexciton binds to two CB holes and a satellite electron.

Figure 4

(a) Log-scale color map of the photoluminescence intensity in electron-doped $\mathrm{ML}\text{−}{\mathrm{WSe}}_2$ at 4 K. The hexciton peak, marked with $H$ (often dubbed $X^{-\prime }$ in the literature), emerges around 2 V. The secondary transitions emerge from the dark trion optical transitions, $D^{-}$ and $D_B^{-}$ (see text), and their redshift is enhanced when the peak $H$ emerges. (b) The color map in a larger voltage range, showing the dominance of $H$ in the electron-rich regime. (c) Peak energies of $H$, $D^{-}$, and $D_B^{-}$. The line brightness denotes the normalized PL intensity of the peak and the redshift numbers are in meV per volt.