Evidence of Tomonaga–Luttinger liquid at the folding edge of graphene

Abstract

Searching for systems in which electronic interactions dominate microscopic quantum behaviors is highly desired in condensed matter physics. Here, we provide spectroscopic evidence for the Tomonaga–Luttinger liquid—a state that describes the correlated one-dimensional (1D) electrons—at the tube-like edge with nanoscale width in folded graphene. Using a scanning tunneling microscope, the Tomonaga–Luttinger liquid state is evidenced by the characteristic suppression in the tunneling density of states near the Fermi energy, which exhibits an anomalous power-law scaling with both energy and temperature. We find that the extracted value of the Luttinger parameter K, which defines the interaction strength of the 1D system, is relatively small, around ∼0.16–0.18, as determined using the degeneracy factor of single-wall carbon nanotubes. This K value is comparable to those previously observed in the single-wall carbon nanotubes, indicating a possible strong electronic interaction regime. These results demonstrate that the quasi-1D tube-like structure at the folding edge of graphene can mimic the electronic properties of well-confined 1D carbon nanotubes. Our work therefore establishes graphene folding edge as an alternative platform to study emergent correlated physics in 1D.