In solids, electronic Bloch states are formed by atomic orbitals. While it is natural to expect that orbital composition and information about Bloch states can be manipulated and transported, in analogy to the spin degree of freedom extensively studied in past decades, it has been assumed that orbital quenching by the crystal field prevents significant dynamics of orbital degrees of freedom. However, recent studies reveal that an orbital current, given by the flow of electrons with a finite orbital angular momentum, can be electrically generated and transported in wide classes of materials despite the effect of orbital quenching in the ground state. Orbital currents also play a fundamental role in the mechanisms of other transport phenomena such as spin Hall effect and valley Hall effect. Most importantly, it has been proposed that orbital currents can be used to induce magnetization dynamics, which is one of the most pivotal and explored aspects of magnetism. Here, we give an overview of recent progress and the current status of research on orbital currents. We review proposed physical mechanisms for generating orbital currents and discuss candidate materials where orbital currents are manifest. We review recent experiments on orbital current generation and transport and discuss various experimental methods to quantify this elusive object at the heart of $orbitronics$ $-$ an area which exploits the orbital degree of freedom as an information carrier in solid-state devices.
Research Institute of Electrical Communication, Tohoku University（东北大学电气通信研究所）；Center for Science and Innovation in Spintronics, Tohoku University（东北大学自旋电子学创新科学中心）；Department of Physics, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院物理系）；Institut für Physik, Johannes Gutenberg-Universität Mainz（美因茨约翰内斯古腾堡大学物理研究所）；Centre for Quantum Spintronics, Norwegian University of Science and Technology NTNU（挪威科技大学量子自旋电子学中心）
Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学和纳米技术研究所）；Physics Center of Minho and Porto Universities (CF-UM-UP)（米尼奥与波尔图大学物理中心）；International Iberian Nanotechnology Laboratory (INL)（伊比利亚国际纳米技术实验室）
Quantum geometric origins of the orbital degrees of freedom of hybrid bosonic quasiparticles in magnetic systems
University of Delaware（特拉华大学）；Quy Nhon University（归仁大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）；University of Maryland, College Park（马里兰大学帕克分校）
Nonlocal Electrical Detection of Reciprocal Orbital Edelstein Effect
The University of Tokyo（东京大学）；RIKEN（理化学研究所）；National Institute of Advanced Industrial Science and Technology (AIST)（国立先进工业科学技术研究院）；Pohang University of Science and Technology（浦项科技大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Johannes Gutenberg University Mainz（美因茨约翰内斯古腾堡大学）；Forschungszentrum Jülich（于利希研究中心）
Extrinsic Orbital Hall Effect and Orbital Relaxation in Mesoscopic Devices
Universidade Federal Rural de Pernambuco（巴西联邦农村大学）；Pohang University of Science and Technology (POSTECH)（韩国科学技术院）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Physics Center of Minho and Porto Universities (CF-UM-UP)（米尼奥与波尔图大学物理中心）；International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术国际实验室）
Evidence for strong localization of orbital polarization
State Key Laboratory of Semiconductor Physics and Chip Technologies, Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所半导体物理与芯片技术国家重点实验室）；Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电工程学院）；College of Physics and Information Technology, Shaanxi Normal University（陕西师范大学物理与信息科学学院）
Observation of Orbit-Orbit Torques: Highly Efficient Torques on Orbital Moments Induced by Orbital Currents
School of Materials Science and Engineering, Beihang University（北京航空航天大学材料科学与工程学院）；State Key Laboratory of Tropic Ocean Engineering Materials and Materials Evaluation, Beihang University（北京航空航天大学热带海洋工程材料与材料评估国家重点实验室）
Inverse Orbital Torque via Spin-Orbital Entangled States
虽然在各种结构中已经通过实验发现了轨道电流引起的电流转矩，但迄今为止还没有证据证明其相互作用。在这里，我们报告的YIG/Pt/CuOx（YIG = Y3 Fe 5 O 12）介导的Pt中的自旋轨道纠缠电子态的强逆轨道力矩的实验证据。通过铁磁共振自旋泵浦和自旋Seebeck效应从YIG向Pt注入自旋电流，我们发现了明显的反自旋霍尔效应信号。虽然部分信号被解释为由于Pt中的逆自旋轨道霍尔效应，但我们也发现与YIG/Pt中的信号相比，YIG/Pt/CuOx结构中的信号显著增加。我们将其归因于Pt中自旋轨道纠缠态介导的Pt/CuOx界面的逆轨道Rashba-Edelstein效应。我们的工作为理解非平衡态下的自旋轨道纠缠物理铺平了道路，并为轨道电子器件应用中的轨道电流的电检测提供了一种方法。
Gauge-covariant theory of the orbital Hall effect: role of itinerant orbital currents and a non-Kubo contribution
Peter Grünberg Institut, Forschungszentrum Jülich（彼得·格林伯格研究所，于利希研究中心）；Institute of Physics, Johannes Gutenberg-University Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；Department of Physics, RWTH Aachen University（亚琛工业大学物理系）；Department of Physics, Pohang University of Science and Technology（浦项科技大学物理系）；Center for Quantum Dynamics of Angular Momentum（角动量量子动力学中心）；Department of Physics, Korea University（韩国大学物理系）
Giant Intrinsic Spin and Orbital Hall Effects in Sr2MO4 (M=Ru,Rh,Mo)
通过研究金属d电子体系中Sr 2 MO 4（M=Ru，Rh，Mo）的t_{2g}轨道紧束缚模型，研究了金属d电子体系的本征自旋霍尔电导（SHC）和d轨道霍尔电导（OHC）.所得到的电导率比空穴掺杂5%的p型半导体的预测值大一到两个数量级。这些巨大的霍尔效应的起源是"有效Aharonov-Bohm相位“，这是由d原子角动量与自旋轨道相互作用和轨道间跳跃积分引起的。这种机制产生的巨大的SHC和OHC有望普遍存在于多轨道过渡金属配合物中，这为实现自旋电子学和轨道电子学器件提供了可能性。
