Quantum Hall Resistance and Quantum Hall Plateaus from Edge State Quantization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911098034192384 |
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| author | Pereyra, Pedro |
| author_facet | Pereyra, Pedro |
| contents | Despite the extensive literature on the quantum Hall effect (QHE), a direct derivation of the phenomenological formula $ρ_{xy} = h/e^2ν$ from first principles has remained elusive. In this work, we revisit the Landau and Landauer-Büttiker formalisms and impose hard-wall boundary conditions on the wavefunction, an essential but often overlooked constraint. This condition quantizes the guiding center position and the longitudinal wave number $k_x$, leading naturally to a discrete number of edge states without invoking energy bending. We derive the Hall resistance directly and recover the standard result $ρ_{xy} = h/e^2ν$, along with an explicit expression for the filling factor $ν$ in terms of the Fermi energy and magnetic field. The resulting resistance steps reproduce the observed QHE plateaus and match experimental data without fitting parameters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_05912 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Hall Resistance and Quantum Hall Plateaus from Edge State Quantization Pereyra, Pedro Mesoscale and Nanoscale Physics Materials Science Despite the extensive literature on the quantum Hall effect (QHE), a direct derivation of the phenomenological formula $ρ_{xy} = h/e^2ν$ from first principles has remained elusive. In this work, we revisit the Landau and Landauer-Büttiker formalisms and impose hard-wall boundary conditions on the wavefunction, an essential but often overlooked constraint. This condition quantizes the guiding center position and the longitudinal wave number $k_x$, leading naturally to a discrete number of edge states without invoking energy bending. We derive the Hall resistance directly and recover the standard result $ρ_{xy} = h/e^2ν$, along with an explicit expression for the filling factor $ν$ in terms of the Fermi energy and magnetic field. The resulting resistance steps reproduce the observed QHE plateaus and match experimental data without fitting parameters. |
| title | Quantum Hall Resistance and Quantum Hall Plateaus from Edge State Quantization |
| topic | Mesoscale and Nanoscale Physics Materials Science |
| url | https://arxiv.org/abs/2508.05912 |