Disordered topological quantum critical points in three-dimensional systems

Details Disordered topological quantum critical points in three-dimensional systems Disordered topological quantum critical points in three-dimensional systems

2010-01-14

arxiv.org/abs/1001.2442v1

New Journal of Physics, {\bf 12}, 065008 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

20 pages (single column), 5 figures, submitted to New Journal of Physics

Scientific paper

10.1088/1367-2630/12/065008

Generic non-magnetic disorder effects onto those topological quantum critical points (TQCP), which intervene the three-dimensional topological insulator and an ordinary insulator, are investigated. We first show that, in such 3-d TQCP, any backward scattering process mediated by the chemical-potential-type impurity is always canceled by its time-reversal (T-reversal) counter-process, because of the non-trivial Berry phase supported by these two processes in the momentum space. However, this cancellation can be generalized into only those backward scattering processes which 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 bulk-edge correspondence. Motivated by this, we further derive the self-consistent-Born phase diagram in the presence of generic non-magnetic disorder potentials and argue the behaviour of the quantum conductivity correction in such cases. The distinction and similarity between the case with only the chemical-potential-type disorder and that with the generic non-magnetic disorders are finally summarized.

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