Effects of quantum deformation on the integer quantum Hall effect

Understand

In this work an application of the $\kappa$--deformed algebra in condensed matter physics is presented.

• Starting by the $\kappa$--deformed Dirac equation we study the relativistic generalization of the $\kappa$--deformed Landau levels as well as the consequences of the deformation on the Hall conductivity.
• By comparing the $\kappa$--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 $\kappa$--deformed Hall conductivity of a 2DEG is obtained as well.