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Classical spins in topological insulators

Following the recent theoretical proposal and experiment on quantum spin Hall effect in HgTe/CdTe quantum wells, we consider a single magnetic impurity localized in the bulk of the system, which we treat as a classical spin. It is shown that there are always localized excited states in the bulk energy gap for arbitrarily strong impurity strength in inverted region, while the localized excited states vanish for very strong impurity strength in normal region. Similar conclusion also applies to three-dimensional topological insulators. This distinct difference serves as another novel criterion for the conventional and topological insulating phases when the time-reversal symmetry is broken, and can be easily experimentally observed through the STM and/or ARPES experiments.