UC San Diego

The interaction between symmetry and topology is deep, and at the heart of both are the dual domains of real and reciprocal space. This dissertation aims to explore and explain the effects that symmetry has on topological phases of matter from both perspectives. To make these problems amenable to calculation and experiment, the platform of periodic engineered media, including photonic and phononic crystals, have been used. They provide a rich and highly efficient means of probing the different behaviors that different topological aspects can have on systems with given sets of symmetries.