Atomically thin transition metal dichalcogenides (TMDs, e.g. MoS$_2$, MoSe$_2$, WSe$_2$, and NbSe$_2$) exhibit remarkable properties which are relevant for science and novel applications, such as robust excitonic effects and well-defined valley degree of freedom. These electronic and vibrational properties are highly dependent on the layer number, stacking configuration, and charge density in the sample system and may be probed and manipulated through applied electromagnetic fields. As the quality and complexity of TMD-based devices has improved, so too has our ability explore the novel physics of these systems. In this dissertation, we probe exceptionally high-quality TMD devices to explore the detailed excitonic physics in monolayer WSe$_2$ and the interlayer phonons in MoS$_2$ and NbSe$_2$.

First, we study monolayer WSe$_2$ devices encapsulated in boron nitride. The WSe$_2$ optical spectra exhibit diverse excitonic features, including the bright states, both the intra- and inter-valley dark states, and a collection of phonon replicas. We systematically study these spectral features and identify novel excitonic physics. For the bright states, we observe the 1s – 4s Rydberg excitons and measure their binding energy and exciton radii. When subject to high magnetic field, the bright trions (or exciton polarons) further exhibit pronounced charge-density-dependent oscillations due to Landau quantization. For the dark states, we identify the dark trions and demonstrate their distinct valley Zeeman effect and enhanced lifetime compared to bright trions. We further observe the intervalley exciton and characterize the intra- and inter-valley relaxation pathways available to the dark states. Finally, we investigate the exciton-phonon interactions and observe a collection of phonon-mediated relaxation processes. We demonstrate that these phonon replicas enable valley-selective optical detection of the dark excitons (trions).

Beyond the monolayer, we study the interlayer shear and breathing mode phonons in multilayer MoS$_2$ and NbSe$_2$. We compare the phonon spectra of 2H- and 3R-stacked MoS$_2$ crystals and observe strong dependence of the shear modes on the layer stacking order. We further simulate the Raman spectra with a concise analytical model that considers the layer-by-layer structure of 2D crystals. Our Raman results provide an effective method to characterize the layer number and stacking order in 2D materials.