Together with Timo Hyart and later with Peter Silvestrov I argued that electron-electron interactions are important for quantum spin Hall (QSH) insulators. In particular, in the time-reversal invariant case the interactions can spontaneously break time-reversal symmetry and induce elastic backscattering in the QSH edge. In the presence of external perpendicular magnetic field we have proposed a novel helical quantum Hall exciton condensate state with confined fractional edge excitations. Though first signatures of the exciton condensation are claimed to be observed in the QSH systems, there is still a lot to be done from both theory and experiment sides to establish the properties of the system.
Below are the pseudospin excitations in the helical quantum Hall exciton condensate. Pseudospin direction determines where the electron is sitting in the bilayer system, electron or hole layer.
(c) NPG, figure adopted from Nature Communications 7, 10462 (2016)