https://doi.org/10.1140/epjp/s13360-025-06842-8
Regular Article
Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg–Witten map
Department of Physics, West Bengal State University, Barasat, 700126, Kolkata, India
Received:
22
April
2025
Accepted:
10
September
2025
Published online:
27
September
2025
We investigate the relativistic quantum dynamics of a massless 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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
