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Abstract 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 one-dimensional defects 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 within defectively engineered WS₂atop graphene, where band structure and the atomic environment is visualized with nano angle-resolved photoelectron spectroscopy, scanning tunneling microscopy and 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 one-dimensional metal (1DM) defects. It appears that the vertical heterostructure with graphene and the induced charge transfer from graphene into the 1DM is critical for the formation of a TLL. 

The properties of excitons, or correlated electron–hole pairs, are of paramount importance to optoelectronic applications of materials. A central component of exciton physics is the electron–hole interaction, which is commonly treated as screened solely by electrons within a material. However, nuclear motion can screen this Coulomb interaction as well, with several recent studies developing model approaches for approximating the phonon screening of excitonic properties. While these model approaches tend to improve agreement with experiment, they rely on several approximations that restrict their applicability to a wide range of materials, and thus far they have neglected the effect of finite temperatures. Here, we develop a fully first-principles, parameter-free approach to compute the temperature-dependent effects of phonon screening within the ab initio $\mathit{GW}$-Bethe–Salpeter equation framework. We recover previously proposed models of phonon screening as well-defined limits of our general framework, and discuss their validity by comparing them against our first-principles results. We develop an efficient computational workflow and apply it to a diverse set of semiconductors, specifically AlN, CdS, GaN, MgO, and ${\text{SrTiO}}_3$. We demonstrate under different physical scenarios how excitons may be screened by multiple polar optical or acoustic phonons, how their binding energies can exhibit strong temperature dependence, and the ultrafast timescales on which they dissociate into free electron–hole pairs. 

We introduce a maximally localized Wannier function representation of Bloch excitons, two-particle correlated electron-hole excitations, in crystalline solids, where the excitons are maximally localized with respect to an average electron-hole coordinate in real space. As a proof-of-concept, we illustrate this representation in the case of low-energy spin-singlet and -triplet excitons in cubic lithium fluoride, computed using the ab initio Bethe-Salpeter equation approach. We visualize the resulting maximally localized exciton Wannier functions (MLXWFs) in real space, detail the convergence of the exciton Wannier spreads, and demonstrate how Wannier-Fourier interpolation can be leveraged to obtain exciton energies and states at arbitrary exciton crystal momenta in the Brillouin zone. We further introduce an approach to treat the long-range dipolar coupling between singlet MLXWFs and discuss it in depth. The MLXWF representation sheds light on the fundamental nature of excitons and paves the way toward Wannier-based post-processing of excitonic properties, enabling the construction of ab initio exciton tight-binding models, efficient interpolation of the exciton-phonon vertex, the computation of Berry curvature associated with exciton bands, and beyond.