标题： 相对论电子涡旋束中的自旋-轨道结构和手性异常 显示英文标题

标题： Spin-Orbit Structure and Helicity Anomaly in Relativistic Electron Vortex Beams

摘要： 相对论电子涡旋束（REVB）由于其非平凡的自旋-轨道结构而最近引起了越来越多的关注。 由于相对论电子由狄拉克方程支配，该方程的精确解为理解REVB的角动量特性提供了最可靠的基础。 在本工作中，使用广义级数展开方法，在复数圆柱坐标系中导出了狄拉克方程的一组精确本征解。 我们证明该本征态携带净角动量，涡旋电荷是沿传播方向总角动量的量子数，并推导出内在自旋-轨道耦合强度的显式表达式。 此外，我们表明，螺旋度在涡旋态中表现出异常，可以作为REVB的实际表征量。 这项工作为在理论和实验中进一步探索REVB奠定了理论基础。 显示英文摘要

摘要： The relativistic electron vortex beam (REVB) has attracted increasing attention due to its nontrivial spin-orbit structure recently. As relativistic electrons are governed by the Dirac equation, exact solutions to this equation provide the most reliable starting point for understanding angular momentum characteristics of REVBs. In this work, a set of exact eigensolutions of the Dirac equation are derived in a complex cylindrical coordinate system using a generalized series expansion method. We demonstrate that the eigenstate carries net angular momentum with the vortex charge being the quantum number of the total angular momentum along the propagation direction and deduce the explicit expression for the intrinsic spin-orbit coupling strength. Furthermore, we show that helicity, which exhibits anomaly in the vortex state, can serve as a practical characterizing quantity for the REVB. This work lays a theoretical foundation for further exploration of REVBs in both theory and experiment.