https://doi.org/10.1140/epjp/s13360-025-06698-y
Regular Article
Fermions in 
-dimensions modified by nonminimal coupling and its applications to condensed matter physics
1
Departamento de Ciências Exatas e Naturais, Universidade Estadual do Sudoeste da Bahia, Campus Juvino Oliveira, 45700-00, Itapetinga, BA, Brazil
2
Programa de Pós-graduação em Física, Universidade Federal do Ceará Campus do Pici, 60455-760, Fortaleza, CE, Brazil
3
Programa de Pós-graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, Paraná, Brazil
4
Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, Paraná, Brazil
5
Departamento de Física, Universidade Federal do Paraná, 81531-980, Curitiba, Paraná, Brazil
6
Departamento de Física, Universidade Federal do Maranhão, 65085-580, São Luís, Maranhão, Brazil
Received:
7
April
2025
Accepted:
27
July
2025
Published online:
13
August
2025
Fermions in two-dimensional space, commonly called 
-dimensional fermions, exhibit intriguing and distinctive characteristics that distinguish them from their higher-dimensional counterparts. This paper offers a comprehensive theoretical examination of planar fermionic systems, presenting novel findings by incorporating nonminimal coupling. Our analysis includes the computation of the non-relativistic limit up to second-order corrections in the Dirac equation. We also explore the Schrödinger equation under the influence of a harmonic potential and an electric field. Furthermore, we investigate how the coupling parameter affects physical properties relevant to condensed matter systems. Our results demonstrate that this parameter significantly impacts electronic properties and Hall conductivity. The interplay between an external electric field and the coupling parameter also influences energy levels and the system’s polarizability. These findings underscore the novel effects of including nonminimal coupling in wave equations, offering new insights into the physics of coupled systems.
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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.
