This thesis focuses on the study of the optical response of new atomically thin two-dimensional crystals, principally the family of transition metal dichalcogenides like MoS2. One central theme of the thesis is the precise treatment of the linear and second-order nonlinear optical susceptibilities of atomically thin transition metal dichalcogenides. In addition to their significant scientific interest as fundamental material responses, these studies provide essential knowledge and convenient characterization tools for the application of these 2D materials in opto-electronic devices. Another important theme of the thesis is the valley physics of atomically thin transition metal dichalcogenides. It is shown that the degeneracy in the valley degree of freedom can be lifted and a valley polarization can be created using a magnetic field, which breaks time reversal symmetry in these materials. These findings enhance our basic understanding of the valley electronic states and open up new opportunities for valleytronic applications using two-dimensional materials.
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