Hermitian Bulk – Non-Hermitian Boundary Correspondence

Non-Hermitian band theory distinguishes between line gaps and point gaps. While can give rise to intrinsic non-Hermitian topology without Hermitian counterparts, line-gapped systems always be adiabatically deformed a limit. Here we show that line-gap point-gap intricately connected: topological in $d$ dimensions induce nontrivial on their $(d-1)$-dimensional boundaries when suitable internal spatial symmetries are present. Since essentially realize phases, this establishes correspondence bulk boundary topology. For the hold, no perturbations required itself, so purely Hermitian. Concomitantly, presence of does not affect any results as long they do close gap. On other hand, essential open The then further leads higher-order skin modes, well chiral helical hinge protected by hence unique systems. We identify all symmetry classes where induces an additional is present, establish invariants. There also exist some edge states remain stable, sense even gap cannot boundary.