Effect of strong disorder in a three-dimensional topological insulator: Phase diagram and maps of the Z2 invariant

We study the effect of strong disorder in a three-dimensional topological insulator with time-reversal symmetry and broken-inversion symmetry. First, using level-statistics analysis, we demonstrate the persistence of delocalized bulk states even at large disorder. The delocalized spectrum is seen to display the levitation and pair annihilation effect, indicating that the delocalized states continue to carry the Z(2) invariant after the onset of disorder. Second, the Z(2) invariant is computed via twisted boundary conditions using an efficient numerical algorithm. We demonstrate that the Z(2) invariant remains quantized and nonfluctuating even after the spectral gap becomes filled with dense localized states. In fact, our results indicate that the Z(2) invariant remains quantized until the mobility gap closes or until the Fermi level touches the mobility edges. Based on such data, we compute the phase diagram of the Bi2Se3 topological material as a function of disorder strength and position of the Fermi level.