Institute of Physics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland.
J Phys Condens Matter. 2010 Sep 8;22(35):355602. doi: 10.1088/0953-8984/22/35/355602. Epub 2010 Aug 13.
Although they describe properties of 2D Hall systems in the fractional quantum regime well, composite fermions suffer from the unexplained character of the localized magnetic field flux-tubes attached to each particle in order to reproduce the Laughlin correlations via Aharonov-Bohm phase shifts. The identification of the cyclotron trajectories of 2D charged particles as accessible classical trajectories within the braid group approach at the magnetic field presence, allows, however, for the avoidance of the construction with fluxes. We introduce cyclotron braid subgroups for charged 2D systems at the fractional Landau-level filling associated in a more natural way with composite fermions without invoking field flux-tubes. The Aharonov-Bohm phase shifts caused by fluxes are replaced with the phase gain due to multi-loop cyclotron trajectories unavoidably occurring at the fractional filling of 1/p (p is an odd integer). Another approach to composite particles, using so-called vortices, is also discussed from the point of view of the cyclotron braid group description (for both odd and even p integers).
虽然复合费米子很好地描述了分数量子霍尔系统中的二维霍尔系统的性质，但为了通过阿哈罗诺夫-玻姆相移再现劳林相关性，需要解释附加在每个粒子上的局域磁场通量管的不明特征。然而，在磁场存在的情况下，将二维带电粒子的回旋轨道识别为辫子群方法中可访问的经典轨迹，避免了通量的构造。我们为分数朗道能级填充的二维带电系统引入回旋辫子子群，这种填充方式与复合费米子更自然地相关联，而无需引入磁场通量管。由通量引起的阿哈罗诺夫-玻姆相移被由于在分数填充 1/p（p 是奇数整数）时不可避免地出现的多环回旋轨迹引起的相位增益所取代。另一种使用所谓的涡旋的复合粒子的方法也从回旋辫子群描述的角度进行了讨论（对于奇数和偶数 p 整数）。
