Progress in Physics

Advances in symmetry and topological classification of non-Hermitian systems

LI Guanliang, ZHAO Yujun

2025, 45 (5): 209-222. doi: 10.13725/j.cnki.pip.2025.05.001

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Recent years have witnessed groundbreaking developments in non-Hermitian systems, which transcend the framework of Hermitian operators in conventional quantum mechanics to reveal new physical laws inherent in complex eigenvalues and non-Hermitian symmetries. Unlike Hermitian systems, non-Hermitian systems achieve unified description of dynamical evolution through the real-imaginary dual structure of complex eigenvalues, manifesting unique phenomena including exceptional points, non-orthogonal eigenstates, and the non-Hermitian skin effect (NHSE). These distinctive properties originate from the non-Hermitian nature of their Hamiltonians, such as pseudo-Hermiticity constraining real spectra, the separation of algebraic-geometric multiplicities in Jordan block structures, and the generalized Brillouin zone theory reconstructing bulk-boundary correspondence. Prototypical models like the HatanoNelson model and non-Hermitian Su-Schrieffer-Heeger (SSH) model demonstrate nonreciprocal hopping and topological responses in complex energy spectra, providing paradigmatic platforms for understanding NHSE and energy band singularities. In symmetry and topological classification, non-Hermitian systems extend the traditional Altland-Zirnbauer tenfold classification to the 38-fold Bernard-LeClair symmetry classes, encompassing pseudo-Hermiticity, chiral symmetry, and combined conjugation-transposition operations. Topological classification progresses through dual approaches: K-theory mapping to Hermitian frameworks and homotopy theory analyzing deformation characteristics of complex band manifolds. Future challenges involve developing universal theories for high-dimensional systems, elucidating crystalline symmetry impacts on classification, and implementing experimental platforms, ultimately advancing applications in open quantum systems, nonequilibrium physics, and novel device engineering.

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Advances in optoelectronic devices based on metal halide perovskite thin single crystals

HE Xinyu, BAO Chunxiong

2025, 45 (5): 223-249. doi: 10.13725/j.cnki.pip.2025.05.002

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Metal halide perovskites as a new generation of semiconductor optoelectronic materials, have great potential for applications in solar cells, light-emitting diodes (LEDs), and photodetectors. Typical perovskite photovoltaic devices are mainly based on polycrystalline thin-films. However, the numerous grain boundaries and high defect density in polycrystalline thin films hinder the improvement of device performance. Perovskite thin single-crystalline materials, due to their superior optoelectrical properties such as lower defect density and longer carrier diffusion length compared to polycrystalline thin films, have attracted great attentions in solar cells, photodetectors, X-ray detectors, and lasers. This review systematically introduces the preparation techniques, optimization strategies (component engineering, additive engineering, interface passivation) and device application progress of perovskite thin single-crystalline materials. It focuses on the growth methods and performance regulation of perovskite thin single-crystalline materials. Additionally, it discusses the development of perovskite thin single-crystalline materials as solar cells, photodetectors, X-ray detectors, and as light-emitting devices. Subsequently, it introduces the patterning methods of perovskite thin single-crystal, including inkjet printing and patterning template-induced arraying techniques, as well as the challenges, and looks forward to the future development directions of perovskite thin single-crystal devices.

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Accidental zero modes in a multiorbital superconductor with spin-orbital coupling

XIANG Ke, WANG Da , WANG Qianghua

2025, 45 (5): 250-259. doi: 10.13725/j.cnki.pip.2025.05.003

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The Majorana zero modes in vortex cores are of extensive interest in the context of topological quantum computing. However, a zero-energy bound state may arise accidentally but is not necessarily a Majorana zero mode. Such accidental zero modes should be carefully ruled out in experiment in order to identify the genuine Majorana zero modes. We show that in a spin-orbital coupled multi-band superconductor, such as the iron-selenide superconductor, accidental zero modes indeed arise in the vortex core if the pairing symmetry is the so-called nodeless d-wave (defined in the absence of spin-orbital coupling). Instead, if the pairing symmetry is s₊₊ or s± with respect to the Fermi pockets split by the spin-orbital coupling, the accidental zero modes do not appear in the limit of weak spin-orbital coupling. Our results are not only important in the experimental identification of Majorana zero modes, but also provide an avenue to pinpoint the pairing symmetry of the iron-selenide superconductor.

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