Complex energy structures of exceptional point pairs in two-level systems

¹ Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS) Daejeon 34126, Republic of Korea
² Basic Science Program, Korea University of Science and Technology (UST) - Daejeon 34113, Republic of Korea
³ Department of Physics, Korea Advanced Institute of Science and Technology (KAIST) Daejeon 34141, Republic of Korea

Received: 23 December 2024
Accepted: 9 May 2025

Abstract

We investigate the topological properties of multiple exceptional points in non-Hermitian two-level systems, emphasizing vorticity as a topological invariant arising from complex energy structures. We categorize EP pairs as fundamental building blocks of larger EP assemblies, distinguishing two types: type-I pairs with opposite vorticities and type-II pairs with identical vorticities. By analyzing the branch cut formation in a two-dimensional parameter space, we reveal the distinct topological features of each EP pair type. Furthermore, we extend our analysis to configurations with multiple EPs, demonstrating the cumulative vorticity and topological implications. To illustrate these theoretical structures, we model complex energy bands within a two-dimensional photonic crystal composed of lossy materials, identifying various EP pairs and their branch cuts. These findings contribute to the understanding of topological characteristics in non-Hermitian systems.