Chiral Topological Excitons in a Chern Band Insulator

A family of semiconductors called Chern band insulators are shown to host exciton bands with nonzero topological Chern integers and chiral exciton edge modes. Using a prototypical two-band Chern insulator model, we calculate a linear response function among the density and pseudospin degrees of freedom to obtain the exciton bands and their Chern integers. Eigenvalues of the matrix-formed response function have a well-defined pole below the electron-hole continuum, which describes an energy-momentum dispersion for exciton excitations in the Chern insulator. We define a topological Chern integer for exciton bands from the corresponding eigenvectors. The lowest exciton band acquires the Chern integers such as ±1 and ±2 in the electronic Chern insulator phase. The nontrivial topology can be experimentally observed both by a nonlocal optoelectronic response of exciton edge modes and by a phase shift in the cross-correlation response due to the bulk mode. Our result suggests that magnetically doped HgTe, InAs/GaSb quantum wells, and (Bi,Sb)₂Te₃ thin films are promising candidates for a platform of topological excitonics.