  Noncentrosymmetric nature of single-layer transition metal dichalcogenides
manifest itself in the finite piezoelectricity and valley-Zeeman coupling. We
microscopically model nonlinear exciton transport in nano-bubble of
single-layers of transition metal dichalcogenide. Thanks to the giant
piezoelectric effect, we obtain an enormous internal electric field, $E_{\rm
piezo}\sim 10^7$V/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 leading to the formation of hexagon-shaped
exciton droplet on top of a circularly symmetric nano-bubble. The effect is
tunable via the bubble size dependence of the piezo-electric field $E_{\rm
piezo} \sim h^2_{\rm max}/R^3$ with $h_{\rm max}$ and $R$ being the bubble
height and radius, respectively.
