The electronic spectra of altermagnets are a fertile ground for nontrivial topology due to the unique interplay between time-reversal and crystalline symmetries. This is reflected in the unconventional Zeeman splitting between bands of opposite spins, which emerges in the absence of spin-orbit coupling (SOC) and displays nodes along high-symmetry directions. Here, we argue that even for a small SOC, the direction of the magnetic moments in the altermagnetic state has a profound impact on the electronic spectrum, enabling novel topological phenomena to appear. By investigating microscopic models for two-dimensional (2D) and three-dimensional (3D) altermagnets, motivated in part by rutile materials, we demonstrate the emergence of hitherto unexplored Dirac crossings between bands of the same spin but opposite sublattices. The direction of the moments determines the fate of these crossings when the SOC is turned on. We focus on the case of out-of-plane moments, which forbid an anomalous Hall effect and thus ensure that no weak magnetization is triggered in the altermagnetic state. In the 2D model, the SOC gaps out the Dirac crossings, resulting in mirror Chern bands that enable the Quantum Spin Hall Effect and undergo a topological transition to trivial bands upon increasing the magnitude of the magnetic moment. On the other hand, in the 3D model the crossings persist even in the presence of SOC, forming Weyl nodal loops protected by mirror symmetry. Finally, we discuss possible ways to control these effects in altermagnetic material candidates.
Ferroelectric Altermagnetic Chern Insulator in magnetic field: electrical control of the Chern number
International Research Centre Magtop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所磁顶国际研究中心）；Department of Physics, University of Guilan（吉兰大学物理系）
Resonant-impurity scanning tunneling spectroscopy in altermagnets: dual Fano resonance and Landau-quantization-induced nodal spin contrast
National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics（计算物理国家重点实验室，应用物理与计算数学研究所）；Graduate School, China Academy of Engineering Physics（中国工程物理研究院研究生院）；School of Electronic and Information Engineering, Zhongshan Institute, University of Electronic Science and Technology of China（电子科技大学中山学院电子与信息工程学院）；School of Physics and Physical Engineering, Qufu Normal University（曲阜师范大学物理与光电工程学院）
3D bulk-resolved $g$-wave altermagnetic order parameter in CrSb
Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪什实验室）；Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿强磁场实验室（HLD-EMFL），德累斯顿-罗斯多夫亥姆霍兹中心）；National High Magnetic Field Laboratory（国家高磁场实验室）
研究 CrSb 中非常规磁体的序参量对称性，通过磁量子振荡测量，在 CrSb 布里渊区不同方向旋转磁场，利用其反铁磁带结构特性，精确映射序参量对称性，确立 CrSb 为典型 g 波金属反铁磁体。
Model Hamiltonian for Altermagnetic Topological Insulators
Universidad del Norte（北大学）；Departamento de Física y Geociencias, Universidad del Norte（北大学物理与地球科学系）；Departamento de Matemáticas y Estadística, Universidad del Norte（北大学数学与统计系）
Spin-degenerate bulk bands and topological surface states associated with Dirac nodal lines in RuO2
Tohoku University（东北大学）；Osaka University（大阪大学）；Center for Spintronics Research Network (CSRN), Osaka University（大阪大学自旋电子学研究网络中心）；Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学材料高等研究院）；Center for Science and Innovation in Spintronics (CSIS), Tohoku University（东北大学自旋电子学科学与创新中心）；Toyota Riken–Kyoto University Research Center (TRiKUC)（丰田理研京都大学研究中心）；Indian Institute of Technology (IIT) Kanpur（坎普尔印度理工学院）；Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构物质结构科学研究所）；National Institutes for Quantum Science and Technology (QST)（量子科学技术研究开发机构）；Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University（东北大学先进材料跨学科研究所）
Band topology and symmetry-driven magneto-optical response in two-dimensional d-wave altermagnets with staggered spin-orbit coupling
International Research Centre Magtop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Department of Physics, University of Guilan（吉兰大学物理系）；Institute of Theoretical Physics, Jagiellonian University（雅盖隆大学理论物理研究所）
Quantum anomalous Hall conductivity in altermagnets under applied magnetic field
International Research Centre Magtop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Department of Physics, University of Guilan（吉尔兰大学物理系）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）
Anomalous thermoelectric and thermal Hall effects in irradiated altermagnets
School of Science, Jiangsu University of Science and Technology（江苏科技大学理学院）；State Key Laboratory of Quantum Functional Materials, Department of Physics, and Guangdong Basic Research Center of Excellence for Quantum Science, Southern University of Science and Technology (SUSTech)（南方科技大学量子功能材料国家重点实验室、物理系及广东省量子科学基础研究中心）；Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院物理与应用物理系）
Light-Induced Topological Phase Transitions and Anomalous Thermal Transport in d-Wave Altermagnets
Quaid i Azam University（奎德·阿扎姆大学）；Khazar University（哈扎尔大学）；Zhejiang Normal University（浙江师范大学）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）
Altermagnetic spin textures coupled to superconductors: Domain wall spin-triplet superconductivity and supercurrent-induced torques
Hearne Institute of Theoretical Physics, Department of Physics & Astronomy, Louisiana State University（路易斯安那州立大学物理与天文学系赫恩理论物理研究所）；Institute for Theoretical Physics III, University of Stuttgart（斯图加特大学理论物理第三研究所）
研究与传统 s 波超导体耦合的交变磁体中库珀对形式，考虑交变磁序参量空间不均匀性，发现超导性受交变磁畴影响，有三重态热点等，还存在超电流与交变磁序的相互作用，为相关研究提供独特机会。
Dirac points and Weyl phase in a honeycomb altermagnet
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, Center for Neutron Science and Technology, School of Physics, Sun Yat-Sen University（中山大学物理学院）
Altermagnets Enable Gate-Switchable Helical and Chiral Topological Transport with Spin-Valley-Momentum-Locked Dual Protection
Eastern Institute of Technology（东方理工大学）；University of Science and Technology of China（中国科学技术大学）；Suzhou University of Science and Technology（苏州科技大学）；University at Buffalo, State University of New York（纽约州立大学布法罗分校）
The Connection of Topology between Systems with Different Dimensions: 1D Zak Phases to 2D Chern Number, Weyl Point as the Jumping Channel for One Singularity and Nodal Line to Merge All Singularities
Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers
拓扑人工系统的最新进展为在比通常的三维空间更高的维度上实现拓扑状态打开了大门。在这里，我们提出了一个“张量积”理论，它提供了一种方法来构建任意高的尺寸和陈数的陈绝缘体。特别地，我们证明了$d_A$ D Chern绝缘体$\langle \mathcal{H}_A^{(κ_{A})}, C_A\rangle$与$d_B$ D Chern绝缘体$\langle \mathcal{H}_B^{(κ_B)}, C_B\rangle$的张量积导致$(d_A+d_B)$ D Chern绝缘体$\langle \mathcal{H}_{A B}^{(κ_A\star κ_B)},-2C_AC_B\rangle $，其中在括号中，$\mathcal{H}^{(κ)}$是$d$ D哈密顿量，$C$是相应的$(d/2)$ th Chern数，$κ$标记了五个非手征Altland-Zirnbauer对称类A，AI，D，AII和C。四个实类AI、D、AII和C在乘法“$\star$”下形成克莱因四元群，类AI是单位元，类A是零元。我们的理论导致新的高维拓扑物理。(i)该构造可以生成大的高阶陈数，例如，对于某些情况，所得到的分类是$8\mathbb{Z}$。(ii)有趣的是，边界态的特征是具有非平凡陈荷的平坦节点超曲面。对于所构造的$(d_A+d_B)$ D Chern绝缘体，垂直于$\mathcal{H}…
Linearly Polarized Light-Induced Anomalous Hall Effect and Topological Phase Transitions in an Altermagnetic Topological Insulator
National Laboratory of Solid State Microstructures and School of Physics, Nanjing University（南京大学固体微结构物理学院）；College of Science, China University of Petroleum (East China)（中国石油大学（华东）理学院）；Jiangsu Physical Science Research Center（江苏省物理科学研究院）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学量子信息科学与技术江苏省重点实验室）
