Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg-Witten map
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912612765138944 |
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| author | Halder, Aslam |
| author_facet | Halder, Aslam |
| contents | We investigate the relativistic quantum dynamics of amassless electron in graphene in a two-dimensional noncommutative (NC) plane under a constant background magnetic field. To address the issue of gauge invariance, we employ an effective massless NC Dirac field theory, incorporating the Seiberg-Witten (SW) map alongside the Moyal star product. Using this framework, we derive a manifestly gauge-invariant Hamiltonian for a massless Dirac particle, which serves as the basis for studying the relativistic Landau problem in graphene in NC space. Specifically, we analyze the motion of a relativistic electron in monolayer graphene within this background field and compute the energy spectrum of the NC Landau system. The NC-modified energy levels are then used to explore the system's thermodynamic response. Notably, in the low-temperature limit, spatial noncommutativity leads to a spontaneous magnetization-a distinct signature of NC geometry in relativistic condensed matter systems like graphene. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg-Witten map Halder, Aslam High Energy Physics - Theory Quantum Physics We investigate the relativistic quantum dynamics of amassless electron in graphene in a two-dimensional noncommutative (NC) plane under a constant background magnetic field. To address the issue of gauge invariance, we employ an effective massless NC Dirac field theory, incorporating the Seiberg-Witten (SW) map alongside the Moyal star product. Using this framework, we derive a manifestly gauge-invariant Hamiltonian for a massless Dirac particle, which serves as the basis for studying the relativistic Landau problem in graphene in NC space. Specifically, we analyze the motion of a relativistic electron in monolayer graphene within this background field and compute the energy spectrum of the NC Landau system. The NC-modified energy levels are then used to explore the system's thermodynamic response. Notably, in the low-temperature limit, spatial noncommutativity leads to a spontaneous magnetization-a distinct signature of NC geometry in relativistic condensed matter systems like graphene. |
| title | Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg-Witten map |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2509.23763 |