Spin orbit density wave: A non-magnetic phase of two-dimensional electron gas

We propose and formulate an interaction induced staggered spin-orbit order as a new emergent phase of two-dimensional Fermi gases. We show that when some form of inherent spin splitting via Rashba-type spin-orbit coupling renders two helical Fermi surfaces to become significantly ``nested,'' a Fermi surface instability arises. To lift this degeneracy, a spontaneous symmetry-breaking spin-orbit density wave develops, causing a surprisingly large quasiparticle gapping with chiral electronic states. Since the time-reversal invariant spin-orbit density wave is associated with a condensation energy, quantified by the gap value, destroying such spin-orbit interaction costs sufficiently large magnetic field or temperature or dephasing time. The BiAg$_{\mathrm{2}}$ surface state is shown to be a representative system for realizing such novel spin-orbit interaction. We also apply this theory to LAO/STO interface, Iridates compunds, and in the enigmatic `hidden-order' phase in URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$ T. Das. Phys. Rev. Lett. \textbf{109}, 246406 (2012).