Observation of Quantized Exciton Energies in Monolayer ${\mathrm{WSe}}_2$ under a Strong Magnetic Field

Quantized energy levels are one of the hallmarks of quantum mechanics at the atomic level. The manifestation of quantization in macroscopic physical systems has showcased important quantum phenomena, such as quantized conductance in (fractional) quantum Hall effects and quantized vortices in superconductors. Here we report the first experimental observation of quantized exciton energies in a macroscopic system with strong Coulomb interaction, monolayer ${\mathrm{WSe}}_2$ crystal under a strong magnetic field. Employing helicity-resolved magnetoreflectance spectroscopy, we observe a striking ladder of plateaus as a function of the gate voltage for both exciton resonance in one valley and exciton-polariton branch in the opposite valley, thanks to the inter-Landau levels transitions governed by unique valley-selective selection rules. The observed quantized excitation energy level spacing sensitively depends on the doping level, indicating strong many-body effects. Our work will inspire the study of intriguing quantum phenomena originating from the interplay between Landau levels and many-body interactions in two-dimension monolayer crystals.

Popular Summary

Quantization of fermion energies is understood quite well and has laid the foundation for numerous quantum-based technologies. Less understood is the quantization of excitons—strongly bound pairs of electrons and holes (or electron vacancies) acting as a single particle. To that end, we report the first experimental observation of quantized exciton energies in a system where the Coulomb interaction is strong, namely, in an atomically thin 2D semiconductor.

A strong Coulomb interaction is necessary for studying how excitons behave in the presence of Landau quantization, in which charged particles in a magnetic field can occupy only certain discrete orbits. Landau quantization is at the heart of ubiquitous phenomena such as the quantum Hall effect, which leads to a quantization of conductance that arises in certain materials exposed to large magnetic fields. How excitons fare in the presence of Landau quantization is unknown.

Atomically thin semiconductors known as monolayer transition-metal dichalcogenides (TMDCs) host strongly bound excitons and present an ideal platform for such a study. By reflecting a broadband laser off the surface of a TMDC, we measure its absorption spectra under a large magnetic field perpendicular to the motion of the electrons and holes. The exciton has an energy that appears in the absorption spectra as a peak. We find that the position of this peak jumps as the magnetic field increases, clear evidence that exciton energy is quantized; it has a fixed value depending on the external magnetic field.

With strongly bound excitons now surviving room temperature, future work should think about possible applications, particularly in quantum-information processing. The TMDC system presented in our work, with its new quantum degree of freedom known as “valley spin,” offers a powerful platform for explorations of the rich physics inherent to quantized excitons.

Figure 1

Optical reflectance spectra of the top-gated monolayer ${\mathrm{WSe}}_2$ device. (a) Schematic of the BN (blue) encapsulated monolayer ${\mathrm{WSe}}_2$ device, contacted and top gated by few-layer graphene flakes (black). (b) Schematic of the band structure of monolayer ${\mathrm{WSe}}_2$ at $K$ and $K^{\prime }$ valleys, and the exciton can be selectively excited by the right-circularly polarized (${\sigma }^{+}$) or left-circularly polarized (${\sigma }^{-}$) light. Note that the spin-orbit coupling induced band splittings in the conduction and valence bands are not drawn to their actual scale. (c) The color plot of the optical reflectance spectra as a function of the top-gate voltage. The reflectance spectra were obtained by subtracting the reference reflectance spectra at the gate voltage of $-4\mathrm{V}$ as the background, and the color represents the reflectance intensity difference. $X_0$, $X_0^{2s}$, $X^{+}$, $X_1^{-}$, $X_2^{-}$, and $X^{\prime -}$ correspond to the absorption resonance at the A exciton, $2s$ state of A exciton, the positive trion, intervalley trion, intravalley trion, and the emerging plasmon polaron mode, respectively.

Figure 2

Helicity-resolved optical magnetoreflectance spectra. (a),(b) Color plots of the helicity-resolved optical reflectance spectra for $K$ and $K^{\prime }$ valleys, respectively, as a function of the top-gate voltage with the application of the out-of-plane magnetic field of 25 T. (c) The magnetic field lifts the degeneracy of the $K$ and $K^{\prime }$ valley, and LLs form in the conduction and valence band. The arrows indicate the allowed inter-LL transitions in the $K$ and $K^{\prime }$ valley. Fermi energies of ${\mu }_1$, ${\mu }_2$, ${\mu }_3$, and ${\mu }_4$ correspond to different doping levels controlled by the top-gate voltage.

Figure 3

Magnetoreflectance spectra modified by inter-LL transitions. (a),(b) Enlarged color plots of the helicity-resolved optical reflectance spectra for $K$ (a) and $K^{\prime }$ (b) valleys in Figs. 2 and 2, in the highly $n$-doped region. (c),(d) Enlarged color plots of Figs. 2 and 2 in the $p$-doped region.

Figure 4

Quantized exciton energy and spin- and valley-polarized LLs. (a) Under the out-of-plane magnetic field of 25 T, the reflectance spectra local maximum position was tracked as a function of the gate voltage. The exciton resonance energy as a function of the gate voltage for different LL filling factors exhibits a ladder of plateaus. (b) Integrated exciton differential reflectance intensity as a function of the gate voltage for different filling factors. (c) Integrated reflectance intensity for the exciton-polaron as a function of the gate voltage for different filling factors. (d) Exciton resonance energy as a function of the gate voltage for different magnetic field applied. The plateau feature starts to develop when the magnetic field exceeds 15 T. For each curve in different magnetic fields, we shift the energy of each curve by 4 meV for clarity. (e) The required hole density to completely fill the LL with the filling factor from 1 to 6.