Violations of Bulk-Edge Correspondence for Topological Insulators

Explore the intriguing breakdown of bulk-edge correspondence in topological insulators through this 36-minute lecture by Tom Stoiber from Yeshiva University. Delve into the complexities of continuum models of topological phases, where Hamiltonians act as differential operators under specific local boundary conditions. Discover examples where the number of observed edge modes differs from expectations based on bulk topology. Examine the reasons behind violations of bulk-edge correspondence through boundary condition choices, and investigate mathematical concepts that help explain these anomalies. Gain insights from Stoiber's joint work with Johannes Kellendonk, enhancing understanding of this pivotal concept in topological insulator research.