Non-Hermitian exceptional boundary mode and its application to topological laser Kazuki Sone U. Tokyo We propose an unconventional mechanism to protect gapless edge modes which utilize the nontrivial topology around exceptional points in their edge bands. We term such edge modes as exceptional edge modes because they can robustly exist even if the bulk topology is trivial and thus imply the breakdown of the bulk-boundary correspondence. We also reveal that they are useful as a design principle of topological lasers that amplifies boundary modes in two- and three-dimensional systems.