Boundary conditions for the quantum Hall effect

Angelone G, Asorey M, Facchi P, Lonigro D, Martinez Y (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of Physics A: Mathematical and Theoretical Institute of Physics Publishing (IOP)

Book Volume: 56

Article Number: 025301

Journal Issue: 2

DOI: 10.1088/1751-8121/acb026

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.

Authors with CRIS profile

Davide Lonigro

Involved external institutions

University of Bari Aldo Moro / Università degli Studi di Bari Aldo Moro IT Italy (IT) Universidad de Zaragoza ES Spain (ES)

How to cite

APA:

Angelone, G., Asorey, M., Facchi, P., Lonigro, D., & Martinez, Y. (2023). Boundary conditions for the quantum Hall effect. Journal of Physics A: Mathematical and Theoretical, 56(2). https://dx.doi.org/10.1088/1751-8121/acb026

MLA:

Angelone, Giuliano, et al. "Boundary conditions for the quantum Hall effect." Journal of Physics A: Mathematical and Theoretical 56.2 (2023).

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