Barnett Stephen M
School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom.
Phys Rev Lett. 2017 Mar 17;118(11):114802. doi: 10.1103/PhysRevLett.118.114802. Epub 2017 Mar 13.
The desire to push recent experiments on electron vortices to higher energies leads to some theoretical difficulties. In particular the simple and very successful picture of phase vortices of vortex charge ℓ associated with ℓℏ units of orbital angular momentum per electron is challenged by the facts that (i) the spin and orbital angular momentum are not separately conserved for a Dirac electron, which suggests that the existence of a spin-orbit coupling will complicate matters, and (ii) that the velocity of a Dirac electron is not simply the gradient of a phase as it is in the Schrödinger theory suggesting that, perhaps, electron vortices might not exist at a fundamental level. We resolve these difficulties by showing that electron vortices do indeed exist in the relativistic theory and show that the charge of such a vortex is simply related to a conserved orbital part of the total angular momentum, closely related to the familiar situation for the orbital angular momentum of a photon.
将近期关于电子涡旋的实验推进到更高能量的愿望引发了一些理论难题。特别是，与每个电子的轨道角动量的ℓℏ单位相关联的涡旋电荷为ℓ的相涡旋的简单且非常成功的图景受到了以下事实的挑战：(i) 对于狄拉克电子，自旋和轨道角动量并非分别守恒，这表明自旋 - 轨道耦合的存在会使情况变得复杂；(ii) 狄拉克电子的速度并不像在薛定谔理论中那样简单地是一个相位的梯度，这表明电子涡旋可能在基本层面上并不存在。我们通过表明电子涡旋在相对论理论中确实存在来解决这些难题，并表明这种涡旋的电荷与总角动量的一个守恒轨道部分简单相关，这与光子轨道角动量的常见情况密切相关。
