Boundary conditions for the quantum Hall effect

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.

Automated summary

We propose a self-consistent model for the integer quantum Hall effect on an infinite strip and investigate the influence of finite-size effects on the Hall conductivity using boundary conditions. By exploiting translation symmetry, we determine the spectral properties of the system for a class of boundary conditions and the full spectrum for Robin boundary conditions. Our model reveals the existence of new states with no classical analogues and adds finer structure to the quantization pattern of the Hall conductivity. Additionally, we predict the breakdown of the quantum Hall effect at high values of the applied electric field.