Control of the orbital character of indirect excitons in ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ heterobilayers

Valley selective hybridization and residual coupling of electronic states in commensurate van der Waals (vdW) heterobilayers enable the control of the orbital character of interlayer excitons. We demonstrate electric field control of layer index, orbital character, lifetime, and emission energy of indirect excitons in ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ heterobilayers embedded in an vdW field-effect structure. Different excitonic dipoles normal to the layers are found to stem from bound electrons and holes located in different valleys of ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ with a valley selective degree of hybridization. For the energetically lowest emission lines, coupling of electronic states causes a field-dependent level anticrossing that goes along with a change of the interlayer exciton lifetime from 400 to 100 ns. In the hybridized regime the exciton is delocalized between the two constituent layers, whereas for large positive or negative electric fields, the layer index of the bound hole is field dependent. Our results demonstrate the design of van der Waals solids with the possibility to $\mathit{in}$ situ control their physical properties via external stimuli such as electric fields.

Figure 1

(a) Schematic depiction of the squared moduli of the hole wave functions of the ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ HB at the topmost VB state at the $K$ point $|{\psi }_h^K{\left(\mathit{r}\right)|}^2$ for large negative $\mathit{F}(-)$, vanishing $\mathit{F}\approx 0$, and large positive electric fields $\mathit{F}(+)$. The coupling of electronic hole states results in a field-tunable hybridization and anticrossing behavior of the valence band states at the $K^{\text{VB}}$ point. (b) PL spectra at 10 K for applied voltages $V_G$ of $-4.5$, 0, and 4.5 V. (c) Emission energy of upper and lower exciton branches as a function of $V_G$ indicating the anticrossing behavior. The gray dashed lines indicate the interlayer and intralayer character of the exciton emission. (d) PL lifetime of the $I_{\text{A}}^{\text{lower}}$ emission line as a function of $V_G$, measured at a bath temperature of 10 K (sample 1).

Figure 2

(a) Optical microscope image and schematic depiction of the device structure. The turquoise area indicates the HB area. Scale bar is $10\mu \mathrm{m}$ (sample 1). (b) IX PL spectra for bath temperatures between 290 (dark red) and 4 K (dark blue). The black dashed lines are guides to the eye indicating the emission energy of IXs $I_{\text{A}}, I_{\text{B}}$, and $I_{\text{C}}$ (sample 2).

Figure 3

(a) Emission energies of IXs $I_{\text{A}}, I_{\text{B}}, I_{\text{C}}$, and $I_{\text{D}}$ as a function of bath temperature (sample 2, gray solid dots of the $I_{\text{C}}$ branch sample 1). (b) Voltage-dependent emission energies of IXs at room temperature (sample 1). (c) Schematic band structure of a ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ HB projected onto the atomic orbitals of the individual layers. Blue and purple band colors correspond to ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$ monolayers, while the light-beige color denotes a large degree of hybridization. The anticipated optical interband transitions are marked by arrows.