Emergent Topological order from Spin-Orbit Density wave

We study the emergence of a Z2 -type topological order because of Landau type symmetry breaking order parameter. When two Rashba type SOC bands of different chirality become nested by a magic wavevector [(0,$\backslash $pi) or ($\backslash $pi,0)], it introduces the inversion of chirality between different lattice sites. Such a density wave state is known as spin-orbit density wave[1,2]. The resulting quantum order is associated with the topological order which is classified by a Z2 invariant. So, this system can simultaneously be classified by both a symmetry breaking order parameter and the associated Z2 topological invariant. This order parameter can be realized or engineered in two- or quasi-two-dimensional fermionic lattices, quantum wires, with tunable RSOC and correlation strength. [1] T. Das, PRL 109, 246406 (2012).[2] C. Brand, et al Nature Commun. 6, 8118 (2015).