Exciton Condensation and Charge Fractionalization in a Topological Insulator Film

An odd number of gapless Dirac fermions is guaranteed to exist at a surface of a strong topological insulator such as Bi$_2$Se$_3$ and Bi$_2$Te$_3$. We show that in a thin-film geometry and under external bias, electron-hole pairs that reside in these surface states can condense to form a novel exotic quantum state which we propose to call ``topological exciton condensate'' (TEC). The TEC is similar in general terms to the exciton condensate recently argued to exist in a biased graphene bilayer, but with different topological properties. It exhibits a host of unusual properties including a stable zero mode and a fractional charge $\pm e/2$ carried by a singly quantized vortex in the TEC order parameter.