WS$_2$ Band Gap Renormalization Induced by Tomonaga Luttinger Liquid Formation in Mirror Twin Boundaries

Tomonaga-Luttinger liquid (TLL) behavior in one-dimensional systems has been predicted and shown to occur at semiconductor-to-metal transitions within two-dimensional materials. Reports of mirror twin boundaries (MTBs) hosting a Fermi liquid or a TLL have suggested a dependence on the underlying substrate, however, unveiling the physical details of electronic contributions from the substrate require cross-correlative investigation. Here, we study TLL formation in MTBs within defectively engineered WS$_2$ atop graphene, where band structure and the atomic environment is visualized with nano angle-resolved photoelectron spectroscopy, scanning tunneling microscopy and scanning tunneling spectroscopy, and non-contact atomic force microscopy. Correlations between the local density of states and electronic band dispersion elucidated the electron transfer from graphene into a TLL hosted by MTB defects. We find that MTB defects can be substantially charged at a local level, which drives a band gap shift by $\sim$0.5 eV.