Nonlinear exciton drift in piezoelectric two-dimensional materials

The noncentrosymmetric nature of single-layer (SL) transition-metal dichalcogenides (TMD) manifests itself in the finite piezoelectricity and valley-Zeeman coupling. We microscopically model nonlinear exciton transport in nanobubbles of SL TMDs. Thanks to the giant piezoelectric effect, we obtain an enormous internal electric field, ${E}_{\mathrm{piezo}}\ensuremath{\sim}{10}⁷\phantom{\rule{0.16em}{0ex}}\mathrm{V}/\mathrm{m}$, resulting in a built-in dipole moment of excitons. We demonstrate that the piezo-induced dipole-dipole interaction provides a novel channel for the nonlinear exciton transport distinct from the conventional isotropic funneling of excitons and leads to the formation of a hexagon-shaped exciton droplet on the top of circularly symmetric nanobubbles. Moreover, we found that the hexagonal distribution of exciton density is preserved even for strongly elliptic nanobubbles. The effect is tunable via the bubble-size dependence of the piezoelectric field ${E}_{\mathrm{piezo}}\ensuremath{\sim}{h}_{\mathrm{max}}²/{R}³$ with ${h}_{\mathrm{max}}$ and $R$ being the bubble height and radius, respectively.