Excitonic condensation under spin-orbit coupling and BEC-BCS crossover

The condensation of electron-hole (e-h) pairs is studied at zero temperature and in the presence of a weak spin-orbit coupling (SOC) in the inversion-layer quantum wells. Under realistic conditions, a perturbative SOC can have observable effects in the order parameter of the experimentally long-searched-for excitonic condensate. Firstly, the fermion exchange symmetry is absent for the e-h pairs indicating a counterexample to the known classification schemes of fermion pairing. With the lack of fermion exchange, the condensate spin has no definite parity. Additionally, the excitonic SOC breaks the rotational symmetry yielding a complex order parameter in an unconventional way, i.e. the phase pattern of the order parameter is a function of the condensate density. This is manifested through finite off diagonal components of the static spin susceptibility, suggesting a new experimental method to confirm an excitonic condensate.