Schattschneider P, Schachinger Th, Stöger-Pollach M, Löffler S, Steiger-Thirsfeld A, Bliokh K Y, Nori Franco
1] Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria [2] LMSSMat (CNRS UMR 8579) Ecole Centrale Paris, Châtenay-Malabry F-92295, France [3] University Service Centre for Electron Microscopy, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria.
Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna 1040, Austria.
Nat Commun. 2014 Aug 8;5:4586. doi: 10.1038/ncomms5586.
Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different quantum numbers are produced using nanometre-sized electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction, we reconstruct the rotational dynamics of the Landau wave functions with angular frequency ~100 GHz. We observe that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions.
朗道能级和磁场中电子的状态是凝聚态物理中量子霍尔效应及相关效应背后的基本量子实体。然而，朗道波函数的实空间特性和观测仍然难以捉摸。在此，我们报告了朗道态的实空间观测以及自由电子的内部旋转动力学。在准均匀磁场中，使用纳米级电子涡旋束产生具有不同量子数的态，其半径选择为与朗道态的束腰相匹配。沿着传播方向扫描这些束，我们以约100 GHz的角频率重构了朗道波函数的旋转动力学。我们观察到，具有不同方位角量子数的朗道模式属于三类，分别以零频率、拉莫尔频率和回旋频率旋转为特征。这与经典电子的均匀回旋旋转形成鲜明对比，并且与最近的理论预测完全一致。
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