Volume 116, Number 3, November 2016
|Number of page(s)||6|
|Section||The Physics of Elementary Particles and Fields|
|Published online||09 December 2016|
Effects of quantum deformation on the integer quantum Hall effect
1 Department of Computer Science and Department of Physics and Astronomy, University College London WC1E 6BT London, UK
2 Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa 84030-900 Ponta Grossa, Paraná, Brazil
3 Departamento de Física, Universidade Federal do Maranhão - 65085-580 São Luís, Maranhão, Brazil
4 Departamento de Física, Universidade Federal do Espírito Santo - 29075-910 Vitória, Espírito Santo, Brazil
5 Departamento de Física, Universidade Federal de Lavras - Caixa Postal 3037, 37200-000 Lavras, Minas Gerais, Brazil
Received: 26 July 2016
Accepted: 22 November 2016
In this work an application of the κ-deformed algebra in condensed-matter physics is presented. Starting by the κ-deformed Dirac equation we study the relativistic generalization of the κ-deformed Landau levels as well as the consequences of the deformation on the Hall conductivity. By comparing the κ-deformed Landau levels in the nonrelativistic regime with the energy levels of a two-dimensional electron gas (2DEG) in the presence of a normal magnetic field, upper bounds for the deformation parameter in different materials are established. An expression for the κ-deformed Hall conductivity of a 2DEG is obtained as well. The expression recovers the well-known result for the usual Hall conductivity in the limit . The deformation parameter breaks the Landau levels degeneracy and due to this, it is observed that deformation gives rise to new plateaus of conductivity in a such way that the plateaus widths of the κ-deformed Hall conductivity are less than the usual one. By studying the temperature dependence of the κ-deformed Hall conductivity, we show that an increase of the temperature causes the smearing of the plateaus and a diminution of the effect of the deformation, whilst an increase in the magnetic field enhances the effect of the deformation.
PACS: 11.10.Nx – Noncommutative field theory / 03.65.Pm – Relativistic wave equations / 73.43.-f – Quantum Hall effects
© EPLA, 2016
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