实空间中Hall杆几何与Corbino几何的拓扑不等价性
The topological inequivalence of Hall bar versus Corbino geometries in real space
摘要：
这项工作讨论了直接库仑相互作用的框架中的拓扑结构的影响，考虑两个不同的几何形状，即霍尔酒吧和科尔比诺盘。在研究量子化霍尔效应的主流方法中，相互作用的结果往往被低估。在这里，我们调查的电子数密度，电位和电流分布的屏蔽理论，考虑电子-电子相互作用。包含直接库仑相互作用和现实的边界条件，导致局部金属类可压缩和（拓扑）绝缘体类不可压缩区域。因此，我们表明，这两种几何在坐标空间中的大部分是不可压缩的整个量子化霍尔高原。此外，将两个内接触内的霍尔杆几何形状表明，量子化是不受影响的，通过改变在真实空间中的亏格数。最后，我们提出了新的实验，这将使我们能够区分两个几何形状的拓扑性质的配置空间。
英文摘要：
This work discusses the effect of topology in the frame of direct Coulomb interactions, considering two distinct geometries, namely the Hall bar and the Corbino disc. In the mainstream approaches to the quantized Hall effect, the consequences of interactions are usually underestimated. Here, we investigate the electron number density, potential and current distributions within the screening theory that considers electron-electron interactions. Inclusion of direct Coulomb interaction and realistic boundary conditions result in local metal-like compressible and (Topological) insulator-like incompressible regions. Consequently, we show that the bulk of both geometries in coordinate space is not incompressible throughout the quantized Hall plateau. Furthermore, placing two inner contacts within the Hall bar geometry shows that the quantization is unaffected by changing the genus number in real space. Finally, we propose novel experiments which will enable us to distinguish the topological properties of the two geometries in the configuration space.
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