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

doi:10.1088/1674-1056/ade1c1

中国物理B ›› 2025, Vol. 34 ›› Issue (12): 127304-127304.doi: 10.1088/1674-1056/ade1c1

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

Huiping Wang(王会平)†, Li Ren(任莉), Xiuli Zhang(张修丽), and Liguo Qin(秦立国)

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China

收稿日期:2025-03-12 修回日期:2025-06-04 接受日期:2025-06-06 发布日期:2025-12-09
通讯作者: Huiping Wang E-mail:hp_wang@fudan.edu.cn
基金资助:
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.

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

Huiping Wang(王会平)†, Li Ren(任莉), Xiuli Zhang(张修丽), and Liguo Qin(秦立国)

School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China

Received:2025-03-12 Revised:2025-06-04 Accepted:2025-06-06 Published:2025-12-09
Contact: Huiping Wang E-mail:hp_wang@fudan.edu.cn
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: edge/surface states, bounded systems, bulk-boundary correspondence

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.

Key words: edge/surface states, bounded systems, bulk-boundary correspondence

中图分类号: (Surface states, band structure, electron density of states)

73.20.At

61.50.Ah (Theory of crystal structure, crystal symmetry; calculations and modeling) 73.22.Dj (Single particle states) 02.10.Yn (Matrix theory)

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[J]. 中国物理B, 2025, 34(12): 127304-127304.

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[J]. Chin. Phys. B, 2025, 34(12): 127304-127304.

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

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

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