Dark trions govern the temperature-dependent optical absorption and emission of doped atomically thin semiconductors

Abstract

We perform absorption and photoluminescence spectroscopy of trions in hBN-encapsulated $\mathrm{WS}{\mathrm{e}}_{2}$, ${\mathrm{WS}}_{2},\phantom{\rule{0.28em}{0ex}}\mathrm{MoS}{\mathrm{e}}_{2}$, and $\mathrm{Mo}{\mathrm{S}}_{2}$ monolayers, depending on temperature. The different trends for W- and Mo-based materials are excellently reproduced considering a Fermi-Dirac distribution of bright and dark trions. We find a dark trion, ${X}_{\mathrm{D}}^{\ensuremath{-}}$, 19 meV below the lowest bright trion, ${X}_{1}^{\ensuremath{-}}$, in $\mathrm{WS}{\mathrm{e}}_{2}$ and $\mathrm{W}{\mathrm{S}}_{2}$. In $\mathrm{MoS}{\mathrm{e}}_{2}$, ${X}_{\mathrm{D}}^{\ensuremath{-}}$ lies 6 meV above ${X}_{1}^{\ensuremath{-}}$, while ${X}_{\mathrm{D}}^{\ensuremath{-}}$ and ${X}_{1}^{\ensuremath{-}}$ almost coincide in $\mathrm{Mo}{\mathrm{S}}_{2}$. Our results agree with GW-Bethe-Salpeter equation (GW-BSE) ab initio calculations and quantitatively explain the optical response of doped monolayers with temperature.