Persistent circulating currents in a mesoscopic open ring with side-branch structures are derived by transfer matrix method in the framework of quantum waveguide theory on networks. The behavior of transmission probability may show the Fano resonance in the presence of geometric scattering of side-branch structures. It is shown that persistent circulating currents in the main loop with equal length of both arms in the absence of magnetic flux occur near the Fermi wave vectors where the Fano resonance appears. The numerical results show that a larger persistent current is associated with a stronger Fano resonance. The persistent circulating currents can be controlled by the flux of side-branch structure.

中文翻译：

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具有侧支磁通环的介观开环中的 Fano 共振和持续电流

具有侧支结构的介观开环中的持续循环电流是在网络量子波导理论的框架下通过传递矩阵方法推导出来的。在存在侧枝结构几何散射的情况下，传输概率的行为可能会表现出 Fano 共振。结果表明，在没有磁通量的情况下，在出现 Fano 共振的费米波矢量附近，主回路中双臂长度相等的持续循环电流发生。数值结果表明，较大的持续电流与较强的 Fano 共振相关。持续循环电流可以通过侧枝结构的通量来控制。