Eur. Phys. J. B (2014) 87: 279
https://doi.org/10.1140/epjb/e2014-50439-y

Regular Article

Disorder effect on the quantum Hall effect in thin films of three-dimensional topological insulators

¹ National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, P.R. China
² School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, P.R. China

^a e-mail: njrma@163.com

Received: 30 June 2014
Received in final form: 26 September 2014
Published online: 24 November 2014

Abstract

We numerically study the quantum Hall effect (QHE) in three-dimensional topological insulator (3DTI) thin film in the presence of the finite Zeeman energy g and the hybridization gap Δ under a strong magnetic field and disorder. For Δ = 0 but g ≠ 0, the Hall conductivity remains to be odd-integer quanti-zed σ_xy = ν(e²/h) , where ν = 2ℓ + 1 with ℓ being an integer. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and the higher plateaus disappear first. The two central plateaus with ν = ± 1 around the band center are strongest against disorder scattering. With the increasing of the disorder strength, Hall plateaus are destroyed faster for the system with a weaker magnetic field. If g = 0 but Δ ≠ 0, there is a splitting of the central (n = 0) Landau level, yielding a new plateau with ν = 0, in addition to the original odd-integer plateaus. In the strong-disorder regime, the QHE plateaus can be destroyed due to the float-up of extended levels toward the band center. The ν = 0 plateau around the band center is strongest against disorder scattering, which eventually disappears. For both g ≠ 0 and Δ ≠ 0, the simultaneous presence of nonzero g and Δ causes the splitting of the degenerating Landau levels, so that all integer Hall plateaus ν = ℓ appear. The ν = 0,1 plateaus are the most stable ones. In the strong-disorder regime, all QHE states are destroyed by disorder, and the system transits into an insulating phase.