Wormhole effect in a strong topological insulator

An infinitely thin solenoid carrying magnetic flux Φ (a “Dirac string”) inserted into an ordinary band insulator has no significant effect on the spectrum of electrons. In a strong topological insulator, remarkably, such a solenoid carries protected gapless one-dimensional fermionic modes when Φ=hc/2e . These modes are spin-filtered and represent a distinct bulk manifestation of the topologically nontrivial insulator. We establish this “wormhole” effect by both general qualitative considerations and by numerical calculations within a minimal lattice model. We also discuss the possibility of experimental observation of a closely related effect in artificially engineered nanostructures.