This thesis contains three breakthrough results in condensed matter physics. Firstly, broken reflection symmetry in the hidden-order phase of the heavy-fermion material URu2Si2 is observed for the first time. This represents a significant advance in the understanding of this enigmatic material which has long intrigued the condensed matter community due to its emergent long range order exhibited at low temperatures (the so-called "hidden order"). Secondly and thirdly, a novel collective mode (the chiral spin wave) and a novel composite particle (the chiral exciton) are discovered in the three dimensional topological insulator Bi2Se3. This opens up new avenues of possibility for the use of topological insulators in photonic, optoelectronic, and spintronic devices. These discoveries are facilitated by using low-temperature polarized Raman spectroscopy as a tool for identifying optically excited collective modes in strongly correlated electron systems and three-dimensional topological insulators.
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