Topological Structure of Cherm-Simon Gauge Field and Fractional Statistics

因为在平面系统中不存在内在的自旋统计关系，所以电子可以凝聚而不产生库珀对，我们有可能得到具有分数统计的粒子。将Chern-Simons规范理论应用于平面电子系统，揭示了分数量子霍尔（FractionalQuantumHall，简称FractionalHall）效应的一些新特征：首先，FractionalHall态可以看作玻色化电子的凝聚相;然后，将两个这样的平面电子系统彼此平行放置，我们发现了对应于两层之间的相位差的量子相干相位的自发发展。这种现象与超导体约瑟夫森结中的约瑟夫森现象十分相似。关键的区别在于直流电压电路中的约瑟夫森频率是普通约瑟夫森结中的一半，这反映了玻色化电子的凝聚。(We但我必须指出，迈斯纳效应并不存在。因此，实验验证将证明电子在平面系统中可以不产生库珀对而凝聚的物理原理。我们还分析了平面磁场存在时的激发模式。激发模式被发现是等离子体激元。利用等离子体激元在公度相和非公度相的激发差异，我们解释了贝尔实验室最近发现的激活能相对于平面磁场的异常行为。解释的成功将有力地支持我们对这类系统中约瑟夫森现象的预言。

Because there exists no intrinsic spin-statistics relation in the planar system, it is possible that electrons can condense without making Cooper pairs and that we have particles with fractional statistics. Applying the Chern-Simons gauge theory to the planar electron system, we have revealed some new features of the fractional quantum Hall (FQH) effect.First of all, the FQH state may be considered to be a condensed phase of bosonized electrons. Then, placing two such planar electron systems parallel one to another, we have found a spontaneous development of a quantum coherent phase corresponding to the phase difference between the two layrs. The associated phenomena have a close resemblance to the Josephson phenomena found in superconductor Josephson junction. The crucial difference is that the Josephson frequency in DC-voltage circuit is half of that in the ordinary Josephson junction, as reflects the condensation of bosonized electrons. (We should mention that the Meissner effect does not exist.) Thus, the experimental check will be a proof of the physical principle that electrons can condense without making Cooper pairs in the planar system.We have also analyzed excitation modes in the existence of the in-plain magnetic field. The excitation modes are found to be plasmons. Using the difference of plasmon excitations in the commensurate and incommensurate phases, we have accounted for the anomalous behavior of the activation energy with respect to the in-plain magnetic field, which was recently found at Bell Lab. The success of the explanation will be a strong support for our prediction of the Josephson phenomena in such a system.