Thermal conductivity and the Wiedemann–Franz law in the fractional quantum Hall effect regime around [formula omitted

Abstract

The range of validity of Wiedemann–Franz (WF) law is investigated for the quantum Hall effect regime around ν = 1 / 2 . The composite fermions (CFs) picture along with the appropriate transport theory enables us to use the integer quantum Hall effect and Shubnikov–de Haas conductivity models to calculate the diagonal and non-diagonal components of the electrical and thermal diffusion conductivity tensors. The analysis shows that at ν = 1 / 2 the system and CF components satisfy the Wiedemann–Franz law. The CF components satisfy the Wiedemann–Franz law for the whole range of the low effective magnetic fields while away from ν = 1 / 2 the system components violate it. At high effective magnetic fields the CF components behave exactly as in the integer quantum Hall effect regime. The system’s behavior at high effective magnetic fields violate the Wiedemann–Franz law for any value of the Landau level broadening. This along with the system’s behavior at low fields around ν = 1 / 2 demonstrates the fact that the difference in the physical mechanisms responsible for the Integer and the Fractional quantum Hall effect is reflected upon fundamental physical laws such as the Wiedemann–Franz law.