Strain-induced gauge and Rashba fields in ferroelectric Rashba lead chalcogenide PbX monolayers (X=S, Se, Te)

One of the exciting features of two-dimensional (2D) materials is their electronic and optical tunability through strain engineering. Previously, we found a class of 2D ferroelectric Rashba semiconductors $\mathrm{Pb}X$ ($X=\text{S}$, Se, Te) with tunable spin-orbital properties. In this work, based on our previous tight-binding (TB) results, we derive an effective low-energy Hamiltonian around the symmetry points that captures the effects of strain on the electronic properties of $\mathrm{Pb}X$. We find that strains induce gauge fields which shift the Rashba point and modify the Rashba parameter. This effect is equivalent to the application of in-plane magnetic fields. The out-of-plane strain, which is proportional to the electric polarization, is also shown to modify the Rashba parameter. Overall, our theory connects strain and spin splitting in ferroelectric Rashba materials, which will be important to understand the strain-induced variations in local Rashba parameters that will occur in practical applications.