Higher-order topological insulators

The discovery of topological insulators has rejuvenated band theory and led to fruitful collaboration between theory and experiment. Capitalizing on their inherent insensitivity to local noise, the (d-1)-dimensional surface states of d-dimensional first-order topological insulators remain gapless as long as their protecting symmetries are preserved. In my talk, I will review higher-order topological insulators (HOTIs), which comprise the most recent chapter of topological band theory. They are d-dimensional materials with (d-n)-dimensional gapless boundary states where n > 1. Using minimal examples, I will explain the fundamental types of HOTIs and their symmetry protection. I will also recount some of the exciting experimental results on HOTI (meta-)materials. My talk will be a pedagocical invitation to the field, directed at a broad audience, rather than a comprehensive technical review.