Communication: Multidimensional triple sum-frequency spectroscopy of MoS 2 and comparisons with absorption and second harmonic generation spectroscopies.

Triple sum-frequency (TSF) spectroscopy is a recently developed methodology that enables collection of multidimensional spectra by resonantly exciting multiple quantum coherences of vibrational and electronic states. This work reports the first application of TSF to the electronic states of semiconductors. Two independently tunable ultrafast pulses excite the A, B, and C features of a MoS ₂ thin film. The measured TSF spectrum differs markedly from absorption and second harmonic generation spectra. The differences arise because of the relative importance of transition moments and the joint density of states (JDOS). We develop a simple model and globally fit the absorption and harmonic generation spectra to extract the JDOS and the transition moments from these spectra. Our results validate previous assignments of the C feature to a large JDOS created by band nesting.