Boundary conditions for the quantum Hall effect

• URL: http://arxiv.org/abs/2209.09629v1
• Date: Sat, 17 Sep 2022 12:37:40 GMT
• Title: Boundary conditions for the quantum Hall effect
• Authors: Giuliano Angelone, Manuel Asorey, Paolo Facchi, Davide Lonigro, Yisely Martinez
• Abstract summary: We formulate a self-consistent model of the integer quantum Hall effect on an infinite strip. 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. Our model also predicts the breakdown of the quantum Hall effect at high values of the applied electric field.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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