报告摘要 |
In this talk I will discuss a series of insights into non-equilibrium phenomena involving the orbital angular momentum (OAM) of Bloch electron systems. Recent years have witnessed a surge of interest in the orbital angular momentum of Bloch electrons, motivated by its emerging applications in spintronics and magnetic memory [1]. Magnetic devices utilizing the orbital degree of freedom have the potential to achieve faster and lower power all-electrical operation than current state-of-the-art magnetic memory devices, and the OAM has been shown to be exceedingly long-lived in certain materials. In novel devices magnetic dynamics is driven by orbital torques, which can arise from the orbital magneto-electric effect (OME), a net steady state OAM density induced by an electric field, or the orbital Hall effect (OHE), that is, a net flow of OAM to the boundaries of the sample. At the same time, the OAM has generated considerable interest at the level of basic science. Whereas the equilibrium OAM in a clean system is well understood, fundamental questions surround the OAM of non-equilibrium Bloch electrons, and it is the non-equilibrium OAM that has motivated the recent focus on orbital dynamics. In out-of-equilibrium systems the microscopic physical and topological mechanisms leading to the orbital dynamics are not understood, the relative strengths of Fermi surface and Fermi sea contributions, as well as of intrinsic and extrinsic contributions, are not known, and a fundamental question has loomed over the field regarding the possibility of orbital effects being nonzero in the gap of an insulating material. My talk will address all these issues. I will first show that disorder plays a crucial role in the orbital Hall effect, at least when the OAM current is evaluated according to the conventional prescription of multiplying the matrix elements of the OAM by those of the velocity. The theory of the orbital Hall effect has concentrated overwhelmingly on intrinsic mechanisms. Using a quantum kinetic formulation, I will discuss the intrinsic and extrinsic OHE in the presence of short-range disorder using 2D massive Dirac fermions as a prototype. We have found that, in doped systems, extrinsic effects associated with the Fermi surface (skew scattering and side jump) provide ~ 95% of the OHE. This suggests that, at experimentally relevant transport densities, the OHE is primarily extrinsic [2]. Building on this insight I will show that, more importantly, the conventional evaluation of the orbital Hall effect suffers from a fundamental flaw. Evaluations of the orbital Hall effect have only retained inter-band matrix elements of the position operator. I will outline the correct way to evaluate the OHE including all matrix elements of the position operator, including the technically challenging intra-band elements. Our method recovers previous results and identifies quantum corrections due to the non-commutativity of the position and velocity operators and inter-band matrix elements of the OAM. The quantum corrections dominate the OHE responses of the topological antiferromagnet CuMnAs and of massive Dirac fermions [3]. They also give rise to a giant OHE in the bulk states of topological insulators, which greatly exceeds spin-related effects. I will show that the bulk states give rise to a sizeable OHE that is up to 3 orders of magnitude larger than the spin Hall effect in topological insulators. This is partially because the orbital angular momentum that each conduction electron carries is up to an order of magnitude larger than the ℏ/2 carried by its spin. This result implies that the large torques measured in topological insulator/ferromagnet devices can be further enhanced through careful engineering of the heterostructure to optimise orbital-to-spin conversion [4]. Finally I will discuss our recent insights into the orbital magneto-electric effect. I will show that the OME is partly the result of a non-equilibrium dipole moment generated via Zitterbewegung and proportional to the quantum metric. For tilted massive Dirac fermions this dipole gives the only contribution to the OME in the insulating case, while the intrinsic and extrinsic OMEs occur for different electric field orientations, yielding an experimental detection method. Our results suggest quantum metric engineering as a route towards maximizing orbital torques [5]. In closing I will give an overview of outstanding questions in the field which include the full role of disorder, inhomogeneities, and the non-conservation of the OAM due to intrinsic mechanisms, which our group has also identified [6].
1. Rhonald Burgos Atencia, Amit Agarwal, and Dimitrie Culcer, Advances in Physics X 9, 2371972 (2024). 2. Hong Liu and Dimitrie Culcer, Phys. Rev. Lett. 132, 186302 (2024). 3. Hong Liu, James H. Cullen, Daniel P. Arovas, and Dimitrie Culcer, Phys. Rev. Lett. 134, 036304 (2025). 4. James H. Cullen, Hong Liu, and Dimitrie Culcer, NPJ Spintronics 3, 22 (2025). 5. James H. Cullen, Daniel P. Arovas, Roberto Raimondi, and Dimitrie Culcer, arXiv:2505.02911. 6. Rhonald Burgos Atencia, Daniel P. Arovas, and Dimitrie Culcer, Phys. Rev. B 110, 035427 (2024). |
