Intriguing one-dimensional electronic behavior in emerging two-dimensional materials

Tomonaga–Luttinger liquid (TLL), a peculiar one-dimensional (1D) electronic behavior due to strong correlation, was first studied in 1D nanostructures and has attracted significant attention over the last several decades. With the rise of new two-dimensional (2D) quantum materials, 1D nanostructures in 2D materials have provided a new platform with a well-defined configuration at the atomic scale for studying TLL electronic behavior. In this paper, we review the recent progress of TLL electronic features in emerging 2D materials embedded with various 1D nanostructures, including island edges, domain walls, and 1D moiré patterns. Specifically, novel physical phenomena, such as 1D edge states in 2D transition metal dichalcogenides (TMDs), helical TLL in 2D topological insulators (2DTI), and chiral TLL in 2D quantum Hall systems, are described and discussed at the nanoscale. We also analyze challenges and opportunities at the frontier of this research area.