The Phonon Hall Viscosity is the leading term evincing time-reversal symmetry breaking in the low energy description of lattice phonons. It may generate phonon Berry curvature, and can be observed experimentally through the acoustic Faraday effect and thermal Hall transport. We present a systematic procedure to obtain the phonon Hall viscosity induced by phonon-magnon interactions in magnetic insulators under an external magnetic field. We obtain a general symmetry criterion that leads to non-zero Faraday rotation and Hall conductivity, and clarify the interplay between lattice symmetry, spin-orbit-coupling, external magnetic field and magnetic ordering. The symmetry analysis is verified through a microscopic calculation. By constructing the general symmetry-allowed effective action that describes the spin dynamics and spin-lattice coupling, and then integrating out the spin fluctuations, the leading order time-reversal breaking term in the phonon effective action, i.e. the phonon Hall viscosity, can be obtained. The analysis of the square lattice antiferromagnet for a cuprate Mott insulator, Sr$_2$CuO$_2$Cl$_2$, is presented explicitly, and the procedure described here can be readily generalized to other magnetic insulators.
Phonon Hall Viscosity and the Intrinsic Thermal Hall Effect of $α$-RuCl$_3$
Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Department of Physics, University of Toronto（多伦多大学物理系）；Canadian Institute for Advanced Research（加拿大高级研究院）
Gaussian-Bond Hall Viscosity and Nonlocal Hall Response of a Sampled Landau Level
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论物理研究所）；Institute of Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Department of Physics, Nagoya University（名古屋大学物理学系）；Center for Spintronics Research Network, Keio University（庆应义塾大学自旋电子学研究网络中心）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
Microscopic origin of an exceptionally large phonon thermal Hall effect from charge puddles in a topological insulator
Institute for Topological Insulators, Universität Würzburg（维尔茨堡大学拓扑绝缘体研究所）；II. Physikalisches Institut, Universität zu Köln（科隆大学第二物理研究所）；High Magnetic Field Lab. of Anhui Province, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院安徽省高磁场实验室）；Institute for Theoretical Physics, Universität zu Köln（科隆大学理论物理研究所）
Density-wave order enhances the phonon thermal Hall effect in a trilayer nickelate
Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）；State Key Laboratory of Surface Physics and Department of Physics, Fudan University（复旦大学物理系）；State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；Department of Physics, Tsinghua University（清华大学物理系）
Hall viscosity of the Laughlin state on noisy quantum computers
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；City College of the City University of New York（纽约市立学院）；Western Washington University（西华盛顿大学）；Graduate Center of City University of New York（纽约市立大学研究生中心）
Thermal Hall conductivity of semimetallic graphite dominated by ambipolar phonon drag
Wuhan National High Magnetic Field Center, School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）；Laboratoire de Physique et d’Étude des Matériaux (ESPCI - CNRS - Sorbonne Université), PSL Research University（巴黎高等物理化工学院-法国国家科学研究中心-索邦大学物质物理与研究实验室）
Hall viscosity from metric-sensitive dichroic probes
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico, Universidade de Lisboa（里斯本理工大学）；Advanced Institute for Materials Research (WPI-AIMR), Tohoku University（东北大学先进材料研究所）；Laboratoire Kastler Brossel, Collège de France（法兰西学院卡斯勒-布罗塞尔实验室）；ENS-Université PSL（巴黎高等师范学院-巴黎文理研究大学）；Sorbonne Université（索邦大学）；International Solvay Institutes（国际索尔维研究所）；Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学科际理论数学科学中心）
Resolving Hall and dissipative viscosity ambiguities via boundary effects
我们研究了二维各向异性流体的粘性冗余的物理含义，其中粘度张量的不同分量在系统的主体中导致相同的效应[Rao和Bradlyn，Phys. Rev. X $\textbf{10}$，021005（2020）]。我们首先重新引入冗余，它反映了缺乏知识的系统的微观信息，并给出微观的例子。接下来，我们表明，在系统中的流体流动的边界可以区分，否则冗余的粘性系数。特别是，我们展示了如何分散和阻尼的重力为主的表面波可以用来解决耗散和霍尔粘度之间的冗余，并讨论这些结果如何适用于最近的实验中手性活性流体与非零霍尔粘度。我们的研究结果强调了无发散，磁化样的贡献的重要性的应力（我们称之为“接触条款”）。最后，我们将我们的结果应用到量子霍尔流体的流体动力学，并表明，额外的贡献的行动，使大量的Wen-Zee行动规范不变的系统中的边界可以重新解释的散装粘性冗余。
Thermal Hall Resistivity as a Unifying Description of Phonon Thermal Hall Effect in Various Insulators
Nanyang Technological University（南洋理工大学）；National High Magnetic Field Laboratory, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室国家高磁场实验室）；National High Magnetic Field Laboratory（国家高磁场实验室）；Institute of Science Tokyo（东京科学大学）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
