  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.
