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

doi:10.1088/1674-1056/ade1c1

Abstract 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.

Keywords: edge/surface states bounded systems bulk-boundary correspondence

Received: 12 March 2025
Revised: 04 June 2025
Accepted manuscript online: 06 June 2025

PACS:	73.20.At	(Surface states, band structure, electron density of states)
	61.50.Ah	(Theory of crystal structure, crystal symmetry; calculations and modeling)
	73.22.Dj	(Single particle states)
	02.10.Yn	(Matrix theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11847061) and the Domestic Visiting Program for Young and Middle-aged Teachers in Shanghai Universities.

Corresponding Authors: Huiping Wang
E-mail: hp_wang@fudan.edu.cn

Cite this article:

Huiping Wang(王会平), Li Ren(任莉), Xiuli Zhang(张修丽), and Liguo Qin(秦立国) A non-Hermitian approach for edge/surface states in bounded systems 2025 Chin. Phys. B 34 127304

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