Theory of Excitonic Phases in an Electron-Hole Double-Layer System with Relativistic Spin-Orbit Interaction

We propose helicoidal and helical excitonic insulator phases in a Coulomb-coupled two-dimensional electron-hole double layer (EHDL) system with relativistic spin-orbit interaction. Previously, it was proposed that layered InAs/AlSb/GaInSb heterostructure is an ideal experimental platform for searching excitonic condense phases, while its electron layer has non-negligible Rashba interaction. We clarify that due to the Rashba term, the spin-triplet (spin-1) and spin-singlet (spin-0) excitonic fields in the EHDL system forms either helicoidal or helical structure, depending on its coupling with an in-plane Zeeman field. We provide a comprehensive understanding of electric and magnetic properties of these condensed phases as well as their low-energy collective modes.