Localization structure of electronic states in the quantum Hall effect
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908576657702912 |
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| author | Seye, Alioune Filoche, Marcel |
| author_facet | Seye, Alioune Filoche, Marcel |
| contents | We investigate the localization of electronic states in the integer quantum Hall effect using a magnetic localization landscape (MLL) approach. By studying a continuum Schrödinger model with disordered electrostatic potential, we demonstrate that the MLL, defined via a modified landscape function incorporating magnetic effects, captures key features of quantum state localization. The MLL effective potential reveals the spatial confinement regions and provides predictions of eigenstate energies, particularly in regimes where traditional semiclassical approximations break down. Numerical simulations show that below a critical energy, states localize around minima of the effective potential, while above it, they cluster around maxima-with edge effects becoming significant near boundaries. Bridging the gap between semiclassical intuition and full quantum models, the MLL offers a robust framework to understand transport and localization in disordered quantum Hall systems, and extends the applicability of landscape theory to magnetic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization structure of electronic states in the quantum Hall effect Seye, Alioune Filoche, Marcel Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks We investigate the localization of electronic states in the integer quantum Hall effect using a magnetic localization landscape (MLL) approach. By studying a continuum Schrödinger model with disordered electrostatic potential, we demonstrate that the MLL, defined via a modified landscape function incorporating magnetic effects, captures key features of quantum state localization. The MLL effective potential reveals the spatial confinement regions and provides predictions of eigenstate energies, particularly in regimes where traditional semiclassical approximations break down. Numerical simulations show that below a critical energy, states localize around minima of the effective potential, while above it, they cluster around maxima-with edge effects becoming significant near boundaries. Bridging the gap between semiclassical intuition and full quantum models, the MLL offers a robust framework to understand transport and localization in disordered quantum Hall systems, and extends the applicability of landscape theory to magnetic systems. |
| title | Localization structure of electronic states in the quantum Hall effect |
| topic | Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2508.04528 |