Theory of Luttinger droplets in transition metal dichalcogenide monolayers

Mirror twin boundaries (MTBs), a type of one-dimensional dislocation defects, have been observed in the transition metal dichalcogenide monolayers. Interesting, these MTBs can host quantum valley Hall edge states with restored inversion symmetry and exhibit Luttinger-liquid behavior in transport experiments over a significant temperature range. A more recent STM experiment has revealed that the MTB effective length can be as short as a few nanometers. We theoretically study such MTB Luttinger liquid droplets, obtain the local density-of-state map as a function of energy and position, demonstrate its scaling with the MTB length, and explore the possible effects of tunnelings between two droplets. Our results match well with the experimental findings.