  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 MoS2 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. We develop a simple model and globally fit the absorption and
harmonic generation spectra to extract the joint density of states and the
transition moments from these spectra. Our results validate previous
assignments of the C feature to a large joint density of states created by band
nesting.
