The conventional order parameters in quantum matters are often characterized
by 'spontaneous' broken symmetries. However, sometimes the broken symmetries
may blend with the invariant symmetries to lead to mysterious emergent phases.
The heavy fermion metal URu2Si2 is one such example, where the order parameter
responsible for a second-order phase transition at Th = 17.5 K has remained a
long-standing mystery. Here we propose via ab-initio calculation and effective
model that a novel spin-orbit density wave in the f-states is responsible for
the hidden-order phase in URu2Si2. The staggered spin-orbit order 'spontaneous'
breaks rotational, and translational symmetries while time-reversal symmetry
remains intact. Thus it is immune to pressure, but can be destroyed by magnetic
field even at T = 0 K, that means at a quantum critical point. We compute
topological index of the order parameter to show that the hidden order is
topologically invariant. Finally, some verifiable predictions are presented.Comment: (v2) Substantially modified from v1, more calculation and comparison
with experiments are include