| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry |
| Zhanpeng Lu(陆展鹏)1, Hui Liu(刘辉)2,†, Yan Gu(古燕)3,‡, and Zhihao Xu(徐志浩)2,4,§ |
1 Department of Physics, XinZhou Normal University, Xinzhou 034000, China;
2 Institute of Theoretical Physics and State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University, Taiyuan 030006, China;
3 Shanxi Vocational University of Engineering Science and Technology, Jinzhong 030619, China;
4 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China |
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Abstract The interplay between quasi-periodicity and non-Hermiticity can give rise to rich localization phenomena. In this work, we investigate the localization transition in a one-dimensional nonreciprocal cross-stitch flat band lattice with diagonal quasi-periodic mosaic modulation, which incorporates both constant and quasi-periodic potentials. In general, non-reciprocity induces the skin effect in non-Hermitian systems through nonreciprocal transitions. However, in this work, we find that in a non-reciprocal flat band lattice, when the constant potential is zero, the skin effect does not exist in the system, and the energy spectrum remains purely real and well-defined. In the presence of a non-zero constant potential, we derive analytical solutions for a class of anomalous mobility edges (AMEs) under periodic boundary conditions (PBCs), revealing the systems localization and critical properties. Through analytic results, we demonstrate that the system is fundamentally equivalent to a generalized non-Hermitian Aubry—André (AA) model. Importantly, this equivalence implies the existence of a transition from a critical phase to a localized phase, as predicted by the non-Hermitian AA model. However, our analysis reveals that the transition point from the critical phase to the localized phase is energy-dependent, which fundamentally accounts for the emergence of AMEs. Furthermore, we design a classical electrical circuit to experimentally realize our system. This work provides new insights into localization transitions in non-Hermitian flat band systems.
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Received: 20 August 2025
Revised: 07 November 2025
Accepted manuscript online: 13 November 2025
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PACS:
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71.10.Fd
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(Lattice fermion models (Hubbard model, etc.))
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71.23.An
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(Theories and models; localized states)
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61.44.Br
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(Quasicrystals)
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| Fund: This work is supported by the National Natural Science Foundation of China (Grant Nos. 12375016 and 12461160324), Beijing National Laboratory for Condensed Matter Physics (Grant No. 2023BNLCMPKF001), and the Fundamental Research Program of Shanxi Province (Grant No. 202403021212025). |
Corresponding Authors:
Hui Liu, Yan Gu, Zhihao Xu
E-mail: liuhui99@sxu.edu.cn;guyan@sxgkd.edu.cn;xuzhihao@sxu.edu.cn
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Cite this article:
Zhanpeng Lu(陆展鹏), Hui Liu(刘辉), Yan Gu(古燕), and Zhihao Xu(徐志浩) Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry 2026 Chin. Phys. B 35 077101
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