A non-Hermitian approach for edge/surface states in bounded systems

We suggest and develop a novel approach to determine edge/surface states in bounded systems based on the bulk Hamiltonian of their corresponding unbounded counterparts, where the k-space is extended to the complex k-one. This approach allows us to obtain simple conditions for the existence of edge/surface states in bounded systems. Our analysis also demonstrates that the emergence of such edge/surface states, which are intrinsically linked to the characteristics of system boundaries, cannot manifest without appropriate boundary conditions dictated by the necessity for wave function convergence. In order to demonstrate our method in action, we apply it to study some examples of non-topological and topological edge/surface states. We hope our discussion helps you gain a clearer and more intuitive understanding of the bulk–boundary correspondence.