AI 中文总结
该研究针对含拉什巴自旋-轨道相互作用的两类二维电子系统，证明狄拉克体系的阿哈罗诺夫-卡舍相位为动力学相位，薛定谔体系的该相位为几何相位。
AI 中文摘要
我们考虑两种存在垂直均匀电场的二维（2D）电子系统，该电场会产生拉什巴自旋-轨道相互作用（RSOI）：一种是二维导体中的非相互作用电子系统，用二维薛定谔方程（SE）建模；另一种是单层石墨烯系统，用无质量费米子的二维狄拉克方程（DE）建模。两种情况下，RSOI均通过SU(2)拉什巴矢量势AR表示。我们证明，无论是二维SE还是二维DE，都无法通过规范变换消除AR。不过，对于平面波解，存在一个SU(2)矩阵可从所得的一维SE中消除AR，该幺正矩阵即为阿哈罗诺夫-卡舍（AC）相位因子，可用于在薛定谔框架中计算AC相位。DE的平面波解包含AR的两个分量：沿波矢k方向的AR,k，以及垂直于k方向的AR,n。后者会产生无法从DE中消除的有效电子质量；前者会产生可通过含时幺正变换消除的AC相位。因此，狄拉克AC相位是含时的，即属于动力学相位，这与薛定谔AC相位（几何相位）形成对比。
英文摘要
We consider two two-dimensional (2D) electronic systems in the presence of a perpendicular homogeneous electric field that generates a Rashba spin-orbit interaction (RSOI): a system of non-interacting electrons in a 2D conductor, modeled using the 2D Schrödinger equation (SE), and a single-layer graphene system, modeled using a 2D Dirac equation (DE) for massless fermions. In both cases the RSOI is expressed via an $SU(2)$ Rashba vector potential ${\bf A}_{R}$. We demonstrate that ${\bf A}_{R}$ cannot be eliminated from either the 2D SE or the 2D DE via a gauge transformation. Nevertheless, for a plane wave solution, an $SU(2)$ matrix exists that eliminates ${\bf A}_{R}$ from the resulting 1D SE. This unitary matrix is an Aharonov-Casher (AC) phase factor, and facilitates the calculation of the AC phase in the Schrödinger scheme. The plane wave solution for the DE contains two components of ${\bf A}_{R}$: $A_{R, k}$ in the direction of the wave vector ${\bf k}$, and $A_{R, n}$ normal to ${\bf k}$. The latter generates an effective electron mass that cannot be eliminated from the DE. The former generates an AC phase that can be eliminated by a time-dependent unitary transformation. Thus, the Dirac AC phase is time-dependent, i.e., it is a dynamical phase. This is in contradistinction to the Schrödinger AC phase which is geometrical.
Comments5 pages, 2 eps figures
