Optical fingerprint of dark 2p-states in transition metal dichalcogenides

Atomically thin transition metal dichalcogenides exhibit a remarkably strong Coulomb interaction. This results in a fascinating many-particle physics including a variety of bright and dark excitonic states that determine optical and electronic properties of these materials. So far, the impact of dark states has remained literally in the dark to a large extent, since a measurement of these optically forbidden states is very challenging. Here we demonstrate a strategy to measure a direct fingerprint of dark states even in standard linear absorption spectroscopy. We present a microscopic study on bright and dark higher excitonic states in the presence of disorder for the exemplary material of tungsten disulfide (WS 2 ). We show that the geometric phase cancels the degeneration of 2s and 2p states and that a significant disorder-induced coupling of these bright and dark states offers a strategy to circumvent optical selection rules. As a proof, we show a clear fingerprint of dark 2p states in the absorption spectrum of WS 2 . The predicted softening of optical selection rules through exciton-disorder coupling is of general nature and therefore applicable to related two-dimensional semiconductors.