Department of Physics, Indian Institute of Technology-Kanpur, Kanpur-208 016, India.
J Phys Condens Matter. 2012 May 9;24(18):185304. doi: 10.1088/0953-8984/24/18/185304. Epub 2012 Apr 5.
We study the effect of an in-plane magnetic field on the zitterbewegung (ZB) of electrons in a semiconductor quantum well (QW) and in a quantum dot (QD) with the Rashba and Dresselhaus spin-orbit interactions (SOIs). We obtain a general expression of the time-evolution of the position vector and current of the electron in a semiconductor QW. The amplitude of the oscillatory motion is directly related to the Berry connection in momentum space. We find that in presence of the magnetic field the ZB in a QW does not vanish when the strengths of the Rashba and Dresselhaus SOIs are equal. The in-plane magnetic field helps to sustain the ZB in QWs even at a low value of k(0)d (where d is the width of the Gaussian wavepacket and k(0) is the initial wavevector). The trembling motion of an electron in a semiconductor QW with high Landé g-factor (e.g. InSb) is sustained over a long time, even at a low value of k(0)d. Further, we study the ZB of an electron in QDs within the two sub-band model numerically. The trembling motion persists in time even when the magnetic field is absent as well as when the strengths of the SOI are equal. The ZB in QDs is due to the superposition of oscillatory motions corresponding to all possible differences of the energy eigenvalues of the system. This is an another example of multi-frequency ZB phenomenon.
我们研究了平面磁场对半导体量子阱（QW）和量子点（QD）中电子的 Zitterbewegung（ZB）的影响，这些系统具有 Rashba 和 Dresselhaus 自旋轨道相互作用（SOIs）。我们得到了电子在半导体 QW 中位置矢量和电流随时间演化的一般表达式。振荡运动的幅度与动量空间中的 Berry 连接直接相关。我们发现，在磁场存在的情况下，当 Rashba 和 Dresselhaus SOIs 的强度相等时，QW 中的 ZB 不会消失。平面磁场有助于在 QWs 中维持 ZB，即使在 k(0)d 值较低的情况下（其中 d 是高斯波包的宽度，k(0)是初始波矢）。具有高 Landé g 因子（例如 InSb）的半导体 QW 中的电子的颤抖运动可以持续很长时间，即使在 k(0)d 值较低的情况下也是如此。此外，我们还通过数值方法研究了 QDs 中电子的 ZB 情况，该模型基于双子带模型。即使在没有磁场以及 SOI 强度相等的情况下，电子的颤抖运动也会持续存在。QD 中的 ZB 是由于系统的能量本征值的所有可能差异对应的振荡运动的叠加。这是多频 ZB 现象的另一个例子。
