We establish symmetry-based selection rules for the intrinsic nonlinear thermal Hall effect driven by the quantum metric in altermagnets. We show that a nonvanishing nonlinear thermal Hall conductivity $κ_{xyy}$ requires three conditions: (i) a nontrivial quantum metric, (ii) breaking of mirror symmetry $M_{x}$, and (iii) breaking of twofold rotational symmetry $C_{2}$. Using tight-binding models on a square lattice, we demonstrate that $d$-wave altermagnets naturally break $C_{2}$ through parity-mixing orbital hybridizations, while $g$-wave systems preserve $C_{2}$, forcing the response to vanish identically. Step-by-step Taylor expansions and explicit unitary matrix proofs establish these results. Our framework provides predictive power for material selection and lays the groundwork for nonlinear spin-caloritronic devices.
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；ICTP South American Institute for Fundamental Research（国际理论物理中心南美基础研究所）
Surface-Dominated Anomalous Hall Effect in Altermagnetic MnTe Films
The Pennsylvania State University（宾夕法尼亚州立大学）；Weizmann Institute of Science（魏茨曼科学研究所）；Binghamton University（宾汉姆顿大学）；STFC Rutherford Appleton Laboratory（英国科学与技术设施理事会鲁瑟福阿普尔顿实验室）；National Institute of Standards and Technology（美国国家标准与技术研究院）
Center for Functional Nanomaterials, Brookhaven National Laboratory（布鲁海文国家实验室功能纳米材料中心）；Stony Brook University（石溪大学）；University of Pennsylvania（宾夕法尼亚大学）；Flatiron Institute（平顿研究所）
Spin-to-charge-current conversion in altermagnetic candidate RuO$_2$ probed by terahertz emission spectroscopy
Charles University（查理大学）；Freie Universität Berlin（柏林自由大学）；Czech Academy of Science（捷克科学院）；Bielefeld University（比勒费尔德大学）；Universität Würzburg（维尔茨堡大学）；Materials Science Institute of Barcelona (ICMAB-CSIC)（巴塞罗那材料科学研究所）；Catalan Institute of Nanoscience and Nanotechnology（加泰罗尼亚纳米科学与技术研究所）；University of Nottingham（诺丁汉大学）
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）
Spin-polarized electron transport for the altermagnet CrSb
Institute of Solid State Physics of the Russian Academy of Sciences（俄罗斯科学院固体物理研究所）；V.L. Ginzburg Research Centre for High-Temperature Superconductivity and Quantum Materials, P.N. Lebedev Physical Institute of RAS（俄罗斯科学院P.N.列别杰夫物理研究所V.L.金兹堡高温超导与量子材料研究中心）
Broadband nonlinear Hall response and multiple wave mixing in a room temperature altermagnet
The Hong Kong University of Science and Technology（香港科技大学）；Gifu University（岐阜大学）；Nagoya University（名古屋大学）；The City University of Hong Kong（香港城市大学）；Qingdao University（青岛大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）
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）
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）
