论文标题
霍尔酒吧与科比诺几何形状在真实空间中的拓扑不等度
The topological inequivalence of Hall bar versus Corbino geometries in real space
论文作者
论文摘要
这项工作讨论了拓扑在直接库仑相互作用框架中的影响，考虑到两个不同的几何形状，即Hall Bar和Corbino碟片。在量化大厅效应的主流方法中，相互作用的后果通常被低估。在这里，我们研究了考虑电子电子相互作用的筛选理论中的电子密度，电势和电流分布。包括直接的库仑相互作用和现实的边界条件会导致局部金属样的压缩和（拓扑）绝缘子样不可压缩区域。因此，我们表明，在整个量化的霍尔高原中，坐标空间中的大部分几何形状都不可压缩。此外，将两个内部触点放在霍尔杆的几何形状中表明，该量化不会因更改真实空间中的属数而影响。最后，我们提出了新的实验，这将使我们能够区分配置空间中两个几何形状的拓扑特性。
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.
