Topological, Valleytronic, and Optical Properties of Monolayer PbS

We systematically examine the topological, valleytronic, and optical properties of experimentally accessible PbS (001) few-layers, with a focus on the monolayer. With even-odd layer-dependent oscillations and without band inversions, the band gaps cover a wide spectrum from infrared to visible, making the few-layers promising for optoelectronics. Intriguingly, the uniaxial (biaxial) compressive strain can tune the trivial monolayer into a $\mathcal{Z}_2$-topological (topological crystalline) insulator, which may be utilized for controllable low-power electronic devices. Although elliptical dichroism vanishes in the monolayer due to inversion symmetry, optical pumping provides an efficient tool to characterize the three phases and to realize charge, spin, and valley Hall effects in optoelectronic transport that are tunable by external strain and light ellipticity.