论文标题
量子厅效应的边界条件
Boundary conditions for the quantum Hall effect
论文作者
论文摘要
我们使用边界条件来研究有限大小对霍尔电导率的影响，制定了整数量子霍尔在无限条上的自洽模型。通过利用沿条带的翻译对称性，我们确定系统的一般光谱特性，以符合这种对称性的大量边界条件，以及（纤维）罗宾边界条件的全光谱。特别是，我们发现后者引入了一种没有经典类似物的新状态，并为霍尔电导率的量化模式增加了更精细的结构。此外，我们的模型还可以预测在施加电场的高值下的量子霍尔效应的分解。
We formulate a self-consistent model of the integer quantum Hall effect on an infinite strip, using boundary conditions to investigate the influence of finite-size effects on the Hall conductivity. By exploiting the translation symmetry along the strip, we determine both the general spectral properties of the system for a large class of boundary conditions respecting such symmetry, and the full spectrum for (fibered) Robin boundary conditions. In particular, we find that the latter introduce a new kind of states with no classical analogues, and add a finer structure to the quantization pattern of the Hall conductivity. Moreover, our model also predicts the breakdown of the quantum Hall effect at high values of the applied electric field.
