Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911346577113088 |
|---|---|
| author | Rimon, Emuna Grosfeld, Eytan Lev, Yevgeny Bar |
| author_facet | Rimon, Emuna Grosfeld, Eytan Lev, Yevgeny Bar |
| contents | We study the full distribution of the zero-temperature Hall conductivity in a lattice model of the IQHE using the Kubo formula across disorder realizations. Near the localization-delocalization transition, the conductivity exhibits heavy-tailed fluctuations characterized by a power-law decay with exponent $α\approx 2.3$--$2.5$, indicating a finite mean but a divergent variance. The heavy tail persists across a range of system sizes, correlation lengths of the disorder potential and fillings. Our results demonstrate a breakdown of self-averaging in transport in small, coherent samples near criticality, in agreement with findings in random matrix models of topological indices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions Rimon, Emuna Grosfeld, Eytan Lev, Yevgeny Bar Mesoscale and Nanoscale Physics We study the full distribution of the zero-temperature Hall conductivity in a lattice model of the IQHE using the Kubo formula across disorder realizations. Near the localization-delocalization transition, the conductivity exhibits heavy-tailed fluctuations characterized by a power-law decay with exponent $α\approx 2.3$--$2.5$, indicating a finite mean but a divergent variance. The heavy tail persists across a range of system sizes, correlation lengths of the disorder potential and fillings. Our results demonstrate a breakdown of self-averaging in transport in small, coherent samples near criticality, in agreement with findings in random matrix models of topological indices. |
| title | Heavy-Tailed Hall Conductivity Fluctuations in Quantum Hall Transitions |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2512.24021 |