Wormhole effect in a strong topological insulator

Abstract

An infinitely thin solenoid carrying magnetic flux $\ensuremath{\Phi}$ (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 $\ensuremath{\Phi}=hc/2e$. 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.