Inversion-asymmetric kagome monolayers: A platform for Rashba effect and two-dimensional piezoelectricity

The breathing kagome lattice, a variant of the kagome structure characterized by inversion-symmetry breaking and geometric frustration, provides a fertile ground for realizing unconventional electronic functionalities. Here, using first-principles calculations, we identify 18 stable two-dimensional ${M}_{3}{QX}_{7}$ compounds ($M=\mathrm{Nb}$,Ta; $Q=\mathrm{S}$,Se,Te; $X=\mathrm{Cl}$,Br,I) that host transition-metal-based breathing kagome motifs. Unlike their Mott-insulating, isostructural ${M}_{3}{X}_{8}$ counterparts, these ${M}_{3}{QX}_{7}$ monolayers are nonmagnetic semiconductors driven by molecular-orbital splitting in embedded ${M}_{3}{X}_{12}Q$ clusters. Remarkably, a pronounced Rashba spin splitting (RSS) appears in the lowest conduction band (LCB) and can be effectively tuned via biaxial strain. A k \ifmmode\cdot\else\textperiodcentered\fi{} p analysis shows that the electronic state of the LCB at the \ensuremath{\Gamma} point transforms as the ${E}_{1/2}$ double-group representation of the ${C}_{3v}$ point group, thereby permitting linear-in-$k$ spin-orbit coupling terms that produce the observed RSS. Moreover, ${M}_{3}{QX}_{7}$ monolayers display the rare coexistence of in-plane and out-of-plane piezoelectric responses, in contrast to conventional two-dimensional piezoelectrics whose polarization is confined to the basal plane. The out-of-plane dipole moment (${\ensuremath{\mu}}_{\mathrm{z}}$) and the surface asymmetry in Born effective charges ($|{Z}_{\mathrm{Bottom}}^{*}\ensuremath{-}{Z}_{\mathrm{Top}}^{*}|$) serve as quantitative descriptors of the vertical piezoelectric response, providing a microscopic understanding of its origin. Due to the exceptional mechanical flexibility of this system, both in-plane and out-of-plane responses reach sizeable magnitudes. These findings not only demonstrate the potential of ${M}_{3}{QX}_{7}$ monolayers for integration into spintronic and piezotronic devices, but they also offer new insights into emergent properties in intrinsically inversion-symmetry-broken breathing kagome lattices.