Effects of quantum deformation on the integer quantum Hall effect

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 $\epsilon ={\kappa }^{-1}\to 0$. 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.

arXiv comment6 pages, 7 figures, v3: Title changed, 4 figures added, one table added, discussion on temperature dependence added, matches published version

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Cited by in corpus (6)

• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Two dimensional electron gas in a non-Euclidean space
• Kappa-deformed Dirac oscillator in an external magnetic field
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Rotating effects on the Hall conductivity in a quantum dot