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

TL;DR

This study measures the valley Zeeman effect and diamagnetic shifts in monolayer WS$_2$ and MoS$_2$ at high magnetic fields, revealing exciton properties and providing insights into their electronic structure.

Contribution

First high-field measurements of valley Zeeman splitting and diamagnetic shifts in monolayer WS$_2$ and MoS$_2$, estimating exciton radii and binding energies.

Findings

Zeeman splitting of ~-230 μeV/T with g ≈ -4

Diamagnetic shifts of 0.32 and 0.11 μeV/T² for A and B excitons

Exciton radii of 1.53 nm and 1.16 nm, and binding energies of 410 meV and 470 meV

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.