Quantum spin Hall density wave insulator of correlated fermions

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 $Z_2$ topological invariant. We show that when two oppositely polarized chiral bands [resulting from the Rashba-type spin-orbit coupling ${\alpha }_k$, $k$ is crystal momentum] are significantly nested by a special wavevector $\mathbf{Q}\sim (\pi ,0)/(0,\pi )$, it induces a spatially modulated inversion of the chirality (${\alpha }_{k+Q}={\alpha }_k^{\ast }$) between different sublattices. The resulting quantum order parameters break translational symmetry, but preserve time-reversal symmetry. It is inherently associated with a $Z_2$-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.

8 pages, 4 figures

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Cited by in corpus (1)

• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands