Effects of quantum deformation on the integer quantum Hall effect

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 $\varepsilon=κ^{-1}\to 0$. 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.

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