  The mysterious second order quantum phase transition, commonly attributed to
the `hidden-order' (HO) state, in heavy-fermion metal URu2Si2 exhibits a number
of paradoxical electronic and magnetic properties which cannot be associated
with any conventional order parameter. We characterize and reconcile these
exotic properties of the HO state based on a spin-orbit density wave order
(SODW), constructed on the basis of a realistic density-functional theory (DFT)
band structure. We quantify the nature of the gapped electronic and magnetic
excitation spectrum, in agreement with measurements, while the magnetic moment
is calculated to be zero owing to the spin-orbit coupling induced time-reversal
invariance. Furthermore, a new collective mode in the spin-1 excitation
spectrum is predicted to localize at zero momentum transfer in the HO state
which can be visualized, for example, by electron spin resonance (ESR) at zero
magnetic field or polarized inelastic neutron scattering measurements. The
results demonstrate that the concomitant broken and invariant symmetries
protected SODW order not only provides insights into numerous nontrivial
hidden-order phenomena, but also offers a parallel laboratory to the formation
of a topologically protected quantum state beyond the quantum spin-Hall state
and Weyl semimetals.
