Effects of quantum deformation on the integer quantum Hall effect

TL;DR

This paper explores how quantum deformation via the $$--deformed algebra affects the relativistic Landau levels and Hall conductivity in a 2D electron gas, revealing new conductivity plateaus and bounds on deformation parameters.

Contribution

It introduces a $$--deformed Dirac equation framework to analyze relativistic Landau levels and Hall conductivity, providing new insights into deformation effects in condensed matter systems.

Findings

Deformation breaks Landau level degeneracy.

New conductivity plateaus emerge due to deformation.

Temperature increases smear the plateaus, magnetic field enhances deformation effects.

Abstract

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. The expression recovers the well-known result for the usual Hall conductivity in the limit $\varepsilon=\kappa^{-1}\to 0$. 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 $\kappa$--deformed Hall conductivity are less than the usual one. By studying the temperature dependence of the $\kappa$--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.