Disordered topological quantum critical points in three-dimensional systems

Generic non-magnetic disorder effects on topological quantum critical points (TQCP), which intervene between the three-dimensional (3D) topological insulator and an ordinary insulator, are investigated in this work. We first show that, in such 3D TQCP, any backward-scattering process mediated by chemical-potential-type impurity is always cancelled by its time-reversal (T-reversal) counter-process because of the nontrivial Berry phase supported by these two processes in the momentum space. However, this cancellation can be generalized into only those backward-scattering processes that conserve a certain internal degree of freedom, i.e. the parity density, while the 'absolute' stability of the TQCP against any non-magnetic disorders is required by the bulkedge correspondence. Motivated by this, we further derive the self-consistent Born-phase diagram and the quantum conductivity correction in the presence of generic non-magnetic disorder potentials. The distinctions and similarities between the case with only the chemical-potential-type disorder and that with the generic non-magnetic disorders are summarized.