Staggered Spin-Orbit Order: A New Paradigm of Broken Symmetry Phase of Matter

We propose a novel spin-orbit density wave order, which can arise in a variety of materials classes. In systems where the noninteracting wavefunctions are defined by an exotic quantum number such as total angular momentum, pseudospin, or helical quantum number owing to spin-orbit coupling of various natures, interaction can induce an emergent spin-orbit density wave even when time-reversal symmetry is intact. This density wave order is different from standard time-reversal breaking spin or orbital density wave. We apply this idea to explain the enigmatic “hidden order” phase in heavy fermion URu₂Si₂ as well as an unknown gapped quasiparticle state observed in two-dimensional electron gases, such as the surface state of BiAg₂.