浸没在层级磁通分布中的分形几何
A fractal geometry immersed in a hierarchical magnetic flux distribution
AI总结：
本文研究在层级磁通分布扰动下谢尔宾斯基垫片分形晶格中的量子态与持续电流调控，证明通过调节AB相位层级参数可系统设计量子态并调控持续电流，为分子分形纳米电子器件设计提供理论依据。
摘要：
分形几何在不同长度尺度上呈现出图案的自相似性，这种自相似性广泛存在于自然界中。我们提出了一个谢尔宾斯基垫片（SPG）分形几何的理论模型，其中包含以层级磁通分布形式存在的确定性扰动。这种磁通构型会在电子波函数获得的阿哈罗诺夫-玻姆（AB）相位中诱导出确定性无序。利用紧束缚形式体系，我们证明通过调节这些AB相位的层级参数强度，可以系统地在SPG分形晶格中构建量子态。此外，我们还观察到，通过控制磁通中该层级参数的强度，可以有效地调控SPG分形结构中的持续电流。这一特性在多种填充因子下均成立。我们的结果可能有助于设计利用化学合成技术制备的分子分形结构的纳米电子器件。
英文摘要：
Fractal geometry presents us with a self-similarity in their pattern at various length scales that is prevalent in our natural world. We present theoretical model of a Sierpinski gasket (SPG) fractal geometry with a deterministic perturbation in the form of a hierarchical distribution of magnetic flux. Such flux configuration induces a deterministic disorder in the Aharonov-Bohm (AB) phases picked up by the electron wavefunction. Using the tight-binding formalism, we show that by tunning the strength of the hierarchy parameter of those AB phases, one can systematically engineer quantum states in a SPG fractal lattice. In addition to this, we have also observed that by controlling the strength of this hierarchy parameter in the magnetic flux, one can effectively regulate the persistent current in the SPG fractal structure. This characteristic is found to be true for various filling factors. Our results could be useful for designing nanoelectronic devices using molecular fractal structures fabricated by chemical synthesis technique.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
