Exciton level structure in quantum spin Hall insulators

In many two-dimensional (2D) semiconductors that possess Berry curvature but are topologically trivial (i.e., no protected edge states and zero Chern number), including the commonly studied gapped graphene systems and transition metal dichalcogenides like 2H-MoS₂, a modified hydrogenic-like picture is expected to hold for excitons. Berry curvature effects can split the degeneracy of opposite azimuthal angular momentum m and -m channels, yet the lowest-energy exciton remains the m=0 state with a s-like characteristic. Here, we show this expectation can fail in topologically non-trivial systems, where the electron-hole pair acquires an additional momentum-space phase winding n set by the Berry geometry of the valence and conduction bands. We confirm such behaviours with ab initio GW plus Bethe-Salpeter equation (GW-BSE) calculations on several representative 2D quantum spin Hall insulators.