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

Abstract

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.