Exciton Diamagnetic Shifts and Valley Zeeman Effects in Monolayer WS$_2$ and MoS$_2$ to 65 Tesla (1510.07022v1)

Abstract: We report circularly-polarized optical reflection spectroscopy of monolayer WS$_2$ and MoS$_2$ at low temperatures (4~K) and in high magnetic fields to 65~T. Both the A and the B exciton transitions exhibit a clear and very similar Zeeman splitting of approximately $-$230~$\mu$eV/T ($g\simeq -4$), providing the first measurements of the valley Zeeman effect and associated $g$-factors in monolayer transition-metal disulphides. These results complement and are compared with recent low-field photoluminescence measurements of valley degeneracy breaking in the monolayer diselenides MoSe$_2$ and WSe$_2$. Further, the very large magnetic fields used in our studies allows us to observe the small quadratic diamagnetic shifts of the A and B excitons in monolayer WS$_2$ (0.32 and 0.11~$\mu$eV/T$^2$, respectively), from which we calculate exciton radii of 1.53~nm and 1.16~nm. When analyzed within a model of non-local dielectric screening in monolayer semiconductors, these diamagnetic shifts also constrain and provide estimates of the exciton binding energies (410~meV and 470~meV for the A and B excitons, respectively), further highlighting the utility of high magnetic fields for understanding new 2D materials.

• The paper presents breakthrough measurements detailing significant valley Zeeman splitting and diamagnetic shifts in monolayer WS2 and MoS2 at magnetic fields up to 65 T.
• Utilizing cryogenic circularly-polarized reflection spectroscopy, it quantifies A and B exciton splitting at approximately -230 μeV/T and diamagnetic coefficients of 0.32 and 0.11 μeV/T².
• These results advance theoretical models of 2D exciton behavior and support potential applications in valleytronics and quantum optoelectronics.

Exciton Diamagnetic Shifts and Valley Zeeman Effects in Monolayer WS$_2$ and MoS$_2$ to 65 Tesla

The paper presents an elaborate paper focused on understanding the excitonic properties of monolayer transition-metal disulphides (TMDs), specifically WS$_2$ and MoS$_2$, through their behavior under high magnetic fields, up to 65 Tesla. This work highlights the diamagnetic shifts and valley Zeeman effects observed in these materials, exploring their implications for both fundamental research and potential technological applications.

Key Experimental Findings

The authors employ circularly-polarized optical reflection spectroscopy at cryogenic temperatures to investigate the excitonic transitions in monolayer WS$_2$ and MoS$_2$. They observe significant valley Zeeman splittings in the A and B exciton transitions, both exhibiting a considerable and nearly identical splitting rate of approximately $-$230 μeV/T ($g \simeq -4$). These measurements are particularly crucial as they represent the first documentation of the valley Zeeman effect in monolayer transition-metal disulphides and also provide insights into the B exciton splitting across monolayer TMDs.

Additionally, the research explores the small quadratic diamagnetic shifts of the excitons. The paper analyzes the A and B excitons in monolayer WS$_2$, revealing diamagnetic coefficients of 0.32 and 0.11 μeV/T$^2$, respectively. From these shifts, the research infers the spatial extent of the exciton wavefunctions and estimates their binding energies—410 meV for A excitons and 470 meV for B excitons.

Theoretical Implications and Comparisons

The high magnetic field experiments allow the authors to refine the theoretical understanding of the excitonic phenomena in these materials. The observed valley Zeeman splittings align with theoretical predictions from simple tight-binding models that account for spin and orbital contributions. These models reveal that spin-orbit coupling and valley-specific polarization rules are intricately linked in monolayer TMDs. However, despite the overall agreement, discrepancies in the Zeeman splitting of B excitons hint at the complexity in understanding the excitonic behavior in these 2D systems, warranting further theoretical refinement.

The paper corroborates that the non-local dielectric screening intrinsically affects the exciton binding energies in these 2D materials, deviating from the conventional hydrogenic model and suggesting a non-hydrogenic Rydberg series. This adjustment underscores the essential role that environmental dielectric effects play in modulating exciton properties in monolayer TMDs.

Practical Implications and Future Prospects

The research presented in this paper opens new opportunities to utilize the excitonic properties of monolayer WS$_2$ and MoS$_2$ in practical applications, such as valley-based quantum computing and optoelectronic devices. The findings are pivotal for further experimental investigations aiming to tailor excitonic phenomena through strain engineering, electric field application, or additional environmental alterations. Moreover, the results emphasize the necessity to harness high magnetic fields to understand finer details in 2D material systems effectively.

Moving forward, advancements in this field could aim to explicitly identify the influence of Berry curvature, further dissect the complex role of reduced mass difference between charge carriers, and explore the implications of these findings across other members of the TMD family. Overall, the paper significantly contributes to the ongoing endeavors to elucidate the exciton dynamics in lower-dimensional systems, positioning itself as a precursor to broader experimental and theoretical expansions in the field of 2D materials.