Many-Body Effect of Mesoscopic Localized States in MoS$_2$ Monolayer

Transition metal dichalcogenide monolayers provide an emerging material system to implement quantum photonics with intrinsic two-dimensional excitons or embedded zero-dimensional localized states. Here we demonstrate the mesoscopic localized states between two- and zero- dimensions, which is a many-body system with electron-electron Coulomb interactions. A fine structure splitting is observed, which is similar to quantum dots. Meanwhile the polarization is changed by the magnetic field, due to the nature of two-dimensional monolayers. Furthermore, a large quadratic diamagnetism with a coefficient of around $100\ \mathrm{\mu eV/T^2}$ is observed, as a unique consequence of the mesoscopic scale. The many-body effect also results in the emission energy variation and linewidth narrowing in the spectrum, which corresponds well to the theoretical analysis. These unique properties indicate the great potential of mesoscopic localized states in many-body physics and quantum photonics.