Fine structure and lifetime of dark excitons in transition metal dichalcogenide monolayers

Abstract

The intricate interplay between optically dark and bright excitons governs the light-matter interaction in transition metal dichalcogenide monolayers. We have performed a detailed investigation of the ``spin-forbidden'' dark excitons in ${\mathrm{WSe}}_{2}$ monolayers by optical spectroscopy in an out-of-plane magnetic field ${\mathrm{B}}_{\mathrm{z}}$. In agreement with the theoretical predictions deduced from group theory analysis, magnetophotoluminescence experiments reveal a zero-field splitting $\ensuremath{\delta}=0.6\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ between two dark exciton states. The low-energy state is strictly dipole forbidden (perfectly dark) at ${\mathrm{B}}_{z}=0$, while the upper state is partially coupled to light with $z$ polarization (``gray'' exciton). The first determination of the dark neutral exciton lifetime ${\ensuremath{\tau}}^{\mathrm{D}}$ in a transition metal dichalcogenide monolayer is obtained by time-resolved photoluminescence. We measure ${\ensuremath{\tau}}^{\mathrm{D}}\ensuremath{\sim}110\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.16em}{0ex}}\mathrm{ps}$ for the gray exciton state, i.e., two orders of magnitude longer than the radiative lifetime of the bright neutral exciton at $T=12\phantom{\rule{0.16em}{0ex}}\mathrm{K}$.