Non-Hermitian boundary spectral winding

Spectral winding of complex eigenenergies represents a topological aspect unique in non-Hermitian systems, which vanishes one-dimensional (1D) systems under the open boundary conditions (OBC). In this work, we discover spectral two-dimensional OBC, originating from interplay between Hermitian localization and non-reciprocal pumping. Such nontrivial topology is demonstrated breathing Kagome model with triangle geometry, whose 1D mimics system periodic winding. trapezoidal such can even co-exist corner accumulation edge states, instead extended ones along geometry. An OBC type hybrid skin-topological effect may also emerge provided completely vanishes. By studying Green's function, unveil that be detected response to local driving field, offering realistic method extract for experimental studies.