Topological hybrid electron-hole Cooper pairing

We consider electron--hole Cooper pair condensation in a heterostructure formed by a topological insulator film and a quantum well. We argue that the helical nature of the Dirac electronic states at the topological insulator surface results in the presence of two competing degenerate pairing channels. The corresponding paired states have an unconventional symmetry in the order parameter describing the Cooper pair condensate, can be classified by the topological Chern invariant, and are topologically distinct. We discuss possible manifestations of the nontrivial topology, including the formation of chiral states at the domain walls separating two distinct states, quantized anomalous transport phenomena, and connections with chiral topological superconductivity.