Excitons in Bilayer ${\mathrm{MoS}}_2$ Displaying a Colossal Electric Field Splitting and Tunable Magnetic Response

van der Waals heterostructures composed of transition metal dichalcogenide monolayers (TMDCs) are characterized by their truly rich excitonic properties which are determined by their structural, geometric, and electronic properties: In contrast to pure monolayers, electrons and holes can be hosted in different materials, resulting in highly tunable dipolar many-particle complexes. However, for genuine spatially indirect excitons, the dipolar nature is usually accompanied by a notable quenching of the exciton oscillator strength. Via electric and magnetic field dependent measurements, we demonstrate that a slightly biased pristine bilayer ${\mathrm{MoS}}_2$ hosts strongly dipolar excitons, which preserve a strong oscillator strength. We scrutinize their giant dipole moment, and shed further light on their orbital and valley physics via bias-dependent magnetic field measurements.

Figure 1

(a) Sketch of the device, composed of a few layer graphene, boron nitrite, bilayer ${\mathrm{MoS}}_2$,boron nitrite, few layer graphene sandwhich. (b) Optical micrograph of the sample. (c) Sketch of the exciton states relevant for the optical response in bilayer ${\mathrm{MoS}}_2$ at the $K$ point. At the $K^{\prime }$ point (not shown), the spin bands, which are indicated by the color of the respective bands, are reversed.

Figure 2

(a) Cascade plot of the sample differential reflectivity at various gate voltage. (b) $X^H$ energy with respect to the gate voltage for both dipole orientations (black squares and red dot). The red and black lines are linear fits to the data to extract the dipole size.

Figure 3

(a) Left panel, PL spectra at different gate voltage at 0 magnetic field. The lowest lying emission line corresponds to the trion emission and is denoted $X^{*}$, the neutral intralayer exciton is denoted $X^A$ and the hybrid exciton is denoted $X^H$. Right panel, close up around $X^H$ (b) PL spectra at 0 gate voltage at different magnetic field. Right panel is a close up around $X^H$. (c) Simulated polarization resolved dielectric susceptibility at a magnetic field of $B_z=8\mathrm{T}$.

Figure 4

(a)–(d) Zeeman splittings extracted at various bias conditions (1–2 V) for $X^{*}$ (red square), $X^A$ (blue dot), and $X^H$ green diamond. (e) $g$ factor for $X^H$ with respect to the gate voltage. (f) Model curve for the $g$ factor for $X^H$ with respect to the gate voltage, based on the phenomenological approach introduced in Eq. (9). The two different curves utilize different $g$ factors for the ${\mathrm{MoS}}_2$ $B$ exciton as well as the interlayer exciton.