Abstract
We present the theory of a new type of topological quantum order which is driven by the spin-orbit density wave order parameter, and distinguished by Z₂ topological invariant. We show that when two oppositely polarized chiral bands [resulting from the Rashba-type spin-orbit coupling α_k, k is crystal momentum] are significantly nested by a special wavevector Q∼(π,0)/(0,π), it induces a spatially modulated inversion of the chirality (α_k+Q=α_k^*) between different sublattices. The resulting quantum order parameters break translational symmetry, but preserve time-reversal symmetry. It is inherently associated with a Z₂-topological invariant along each density wave propagation direction. Hence it gives a weak topological insulator in two dimensions, with even number of spin-polarized boundary states. This phase is analogous to the quantum spin-Hall state, except here the time-reversal polarization is spatially modulated, and thus it is dubbed quantum spin-Hall density wave (QSHDW) state. This order parameter can be realized or engineered in quantum wires, or quasi-2D systems, by tuning the spin-orbit couping strength and chemical potential to achieve the special nesting condition.