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

摘要

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 Delta under a strong magnetic field and disorder. For Delta = 0 but g not equal 0, the Hall conductivity remains to be odd-integer quantized sigma(xy) = nu e(2)/h, where nu = 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 nu = +/- 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 Delta not equal 0, there is a splitting of the central (n = 0) Landau level, yielding a new plateau with nu = 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 nu = 0 plateau around the band center is strongest against disorder scattering, which eventually disappears. For both g not equal 0 and Delta not equal 0, the simultaneous presence of nonzero g and Delta causes the splitting of the degenerating Landau levels, so that all integer Hall plateaus nu = l appear. The nu = 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.